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<image>Find the surface area of the solid figure shown. The height is 21 cm.
|
768 \mathrm{cm}^2
|
mathverse_vi_3503
|
|
<image>Find the surface area of the solid figure shown. The height is 20 cm.
|
528 \mathrm{cm}^2
|
mathverse_vi_3508
|
|
<image>Find the surface area of the solid prism. The bottom face has edges of 18cm and 8cm.
|
338 \mathrm{cm}^2
|
mathverse_vi_3513
|
|
<image>Find the surface area of this solid. The thickness of the solid is 3cm.
|
534 \mathrm{cm}^2
|
mathverse_vi_3518
|
|
<image>Find the surface area of the following solid prism. The right rectangle surface has one edge of 10cm.
Give your answer to the nearest one decimal place.
|
577.0 \mathrm{cm}^2
|
mathverse_vi_3523
|
|
<image>Find the total surface area of the solid figure shown.
|
608 \mathrm{cm}^2
|
mathverse_vi_3528
|
|
<image>Find the surface area of the figure shown. The height is 3 cm.
Give your answer to the nearest two decimal places.
|
200.49 \mathrm{cm}^2
|
mathverse_vi_3533
|
|
<image>Find the surface area of the figure shown.
|
120 \mathrm{cm}^2
|
mathverse_vi_3538
|
|
<image>Find the surface area of the solid figure. The height is 6 cm.
Round your answer to one decimal place.
|
256.2 \mathrm{m}^2
|
mathverse_vi_3543
|
|
<image>Find the surface area of the solid shown. The radius is 3cm.
Round your answer to two decimal places.
|
122.52 \mathrm{cm}^2
|
mathverse_vi_3548
|
|
<image>The solid figure has a diameter of 4cm. Find the surface area of the solid formed, correct to two decimal places.
|
91.11 \mathrm{cm}^2
|
mathverse_vi_3553
|
|
<image>Find the surface area of the solid figure. The perpendicular height is 8mm.
Round your answer to two decimal places.
|
288.6 \mathrm{m}^2
|
mathverse_vi_3558
|
|
<image>Find the surface area of the solid figure given. The slant height is 13.7cm.
Give your answer correct to 2 decimal places.
|
651.82 \mathrm{cm}^2
|
mathverse_vi_3563
|
|
<image>Find the surface area of the solid figure shown.
Round your answer to two decimal places.
|
323.10 \mathrm{m}^2
|
mathverse_vi_3568
|
|
<image>Find the surface area of the figure shown, rounded to two decimal places. The height is 12 cm.
|
520.55 \mathrm{cm}^2
|
mathverse_vi_3573
|
|
<image>The middle solid has radius of 6 and height of 11.
Find the surface area of the solid.
Round your answer to two decimal places.
|
8128.50 \text { units }^2
|
mathverse_vi_3578
|
|
<image>Given the following solid. The length of the base is 10cm.
Find the volume of the solid.
|
200 \mathrm{cm}^3
|
mathverse_vi_3583
|
|
<image>Consider the two similar solids shown. The larger solid has a radius of 12 cm.
Find the volume of solid A, in simplest exact form.
|
36\pi \mathrm{cm}^3
|
mathverse_vi_3588
|
|
<image>Consider the two solids shown. The larger solid has a radius of 12 cm.
What is the ratio of the volume of solid A to solid B?
|
1:64
|
mathverse_vi_3593
|
|
<image>Two similar solids as shown in the figure, the larger solid has volumes of 5760\mathrm{cm}^3.
Find the fully simplified ratio of the volume of the larger solid to the volume of the smaller solid.
|
100
|
mathverse_vi_3598
|
|
<image>Consider the solid shown with its height is 12m.
Write a fully expanded and simplified expression for the volume of the solid.
|
12x^2+144x+384 \mathrm{m}^3
|
mathverse_vi_3603
|
|
<image>A solid is shown with the following dimensions. The height of the solid is 5x+7.
Find an expression for L, in terms of the variable, x.
|
\frac{5\left(5x+7\right)}{2x+3} units
|
mathverse_vi_3608
|
|
<image>As shown in the figure, the height of the water tank is 3x. The water tank is leaking at a constant rate of 3\pi x litres per second (where x is a fixed unknown). If the water tank was initially full, calculate the amount of water remaining after \left(2x+2\right)^2 seconds. Give your simplified answer in expanded form.
|
63\pi x^3+66\pi x^2+15\pi x litres
|
mathverse_vi_3613
|
|
<image>Consider the solid shown.
Find the polynomial that represents the volume of the solid.
|
$x^{3}+12 x^{2}+48 x+64$
|
mathverse_vi_3618
|
|
<image>Find the volume of the solid shown, whose height is 8 cm, rounding your answer to two decimal places.
|
Volume $=904.78 \mathrm{~cm}^{3}$
|
mathverse_vi_3623
|
|
<image>Find the volume of the solid shown. The height of the solid is 2cm.
|
$299 \mathrm{~cm}^{3}$
|
mathverse_vi_3628
|
|
<image>As shown in the figure, the height of the solid is 10cm. Calculate the volume of the solid in the figure.
|
$1690cm^2$
|
mathverse_vi_3633
|
|
<image>Find the volume of the solid shown.
|
$144cm^3$
|
mathverse_vi_3638
|
|
<image>As shown in the figure, the height of the solid is 3cm. Find the volume of the solid.
|
48 \mathrm{cm}^3
|
mathverse_vi_3643
|
|
<image>As shown in the figure, the height of the solid is 8cm. Find the volume of the solid.
|
32 \mathrm{cm}^3
|
mathverse_vi_3648
|
|
<image>As shown in the figure, the height of the prism is 2cm. Find the volume of the solid.
|
32 \mathrm{cm}^3
|
mathverse_vi_3653
|
|
<image>As shown in the figure, the height of the solid is 9cm. Find the volume of the solid shown.
|
270 \mathrm{cm}^3
|
mathverse_vi_3658
|
|
<image>As shown in the figure, the height of the base is 14cm. Find the volume of the solid.
|
399 \mathrm{cm}^3
|
mathverse_vi_3663
|
|
<image>As shown in the figure, 2 of segments are cylinders on each side of the solid with radius of 11. Calculate the volume of the solid. Round your answer to one decimal place.
|
1608.5
|
mathverse_vi_3668
|
|
<image>The height of the prism of 16 cm. Find the volume of the composite solid shown.
|
3136 \mathrm{cm}^3
|
mathverse_vi_3673
|
|
<image>The width of the solid in the figure is 9cm. Find the volume of the solid to one decimal place.
|
125.3 \mathrm{cm}^3
|
mathverse_vi_3678
|
|
<image>The height of the solid is 7mm. Find the exact volume of the right solid.
|
\frac{847}{3} \mathrm{mm}^3
|
mathverse_vi_3683
|
|
<image>As shown in the figure, part of the solid is a cone. The height of the cone is 12cm. Find the volume of the composite figure shown, correct to two decimal places.
|
169.65 \mathrm{cm}^3
|
mathverse_vi_3688
|
|
<image>A pyramid has been removed from a solid, as shown in the figure. The height of the solid is 8cm. Find the volume of this composite solid.
|
720 \mathrm{cm}^3
|
mathverse_vi_3693
|
|
<image>Find the height h mm of this closed solid if its surface area (S) is $27288$mm2.
Round your answer to the nearest whole number.
|
58
|
mathverse_vi_3698
|
|
<image>The solid in diagram has a surface area of 54105 \mathrm{mm}^2.
What must the height h mm of the solid be?
Round your answer to the nearest whole number.
|
30
|
mathverse_vi_3703
|
|
<image>A wedding cake consists of three solids stacked on top of each other. The top layer has a height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.
All the sides and top surfaces are to be covered in icing, but not the bottom.
What is the surface area of the cake that needs to be iced?
Give your answer to the nearest cm2.
|
33929 \mathrm{cm}^2
|
mathverse_vi_3708
|
|
<image>A solid is shown with the following dimensions. Height of the solid is 6x+9.
Find an expression for the length L of the base of the solid in terms of the variable, x.
|
24 units
|
mathverse_vi_3713
|
|
<image>Calculate the radius of the sphere shown in figure with the volume of the inside solid 13.75\pi cm3.
|
3
|
mathverse_vi_3718
|
|
<image>The height is 13 cm. Find L. Give your answer rounded down to the nearest cm.
|
14
|
mathverse_vi_3723
|
|
<image>Consider the solid below. Lengths of BC is 4.
Find the length of CX correct to two decimal places.
|
15.81
|
mathverse_vi_3728
|
|
<image>All edges of the following solid have the same length.
Find the exact length of AG in simplest surd form.
|
\sqrt{147}
|
mathverse_vi_3733
|
|
<image>The following is a solid on a square base with side length 16cm. A right solid has its apex aligned directly above the centre of its base.
Find the length of VW, the perpendicular height of the solid correct to two decimal places.
|
23.41
|
mathverse_vi_3738
|
|
<image>A solid has dimensions as labelled on the diagram. The height is 5.
Find the length of AG. Leave your answer in surd form.
|
\sqrt{122}
|
mathverse_vi_3743
|
|
<image>Consider the following figure. The height of the solid is 16cm.
Use Pythagoras' Theorem to find the unknown height $x$ in the solid shown.
|
$x=8 \mathrm{~cm}$
|
mathverse_vi_3748
|
|
<image>In the tube shown above, the circumference of the base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a surface, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38
|
C
|
mathverse_vi_3753
|
|
<image>The figure above shows a solid with height $\sqrt{3} x$. If the volume of the solid is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6
|
A
|
mathverse_vi_3758
|
|
<image>In the figure shown above, the left container has radius of 3. If all the water in the right container is poured into the left container, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2
|
D
|
mathverse_vi_3763
|
|
<image>In the figure above, what is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130
|
C
|
mathverse_vi_3768
|
|
<image>What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72)
|
A
|
mathverse_vi_3773
|
|
<image>What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13
|
E
|
mathverse_vi_3778
|
|
<image>In the figure above. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168
|
C
|
mathverse_vi_3783
|
|
<image>In triangle ABC above. If AB = 6 and BD = 3, what is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree
|
D
|
mathverse_vi_3788
|
|
<image>In the figure above. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85
|
A
|
mathverse_vi_3793
|
|
<image>In the figure above, the circle has radius r. What is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}
|
E
|
mathverse_vi_3798
|
|
<image>In the triangle above, which of the following must be true?
Choices:
A.p=r
B.p<r
C.p>r
D.p=4
E.p>4
|
C
|
mathverse_vi_3803
|
|
<image>In the figure above if the area of triangle CAF is equal to the area of CDEF, what is the length of segment AD?
Choices:
A.7/2
B.5
C.7
D.15/2
E.15
|
C
|
mathverse_vi_3808
|
|
<image>In the figure above, the radii of four circles are 1, 2, 3, and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?
Choices:
A.1:2
B.1:4
C.3:5
D.3:7
E.5:7
|
D
|
mathverse_vi_3813
|
|
<image>If the perimeter of the quadrilateral above is 72, what is the value of x?
Choices:
A.9
B.15
C.18
D.21
E.36
|
C
|
mathverse_vi_3818
|
|
<image>In the figure above. The area of triangle RST is 7 and PT=2/5*PS. What is the area of PQRS?
|
23
|
mathverse_vi_3823
|
|
<image>In the figure above. If 55 < x < 60, what is one possible value of y ?
|
123
|
mathverse_vi_3828
|
|
<image>What fraction of the area of the quadrilateral is shaded?
|
0
|
mathverse_vi_3833
|
|
<image>In the figure above, the area of the shaded region is given by \pi*l*w/4. If the area of the shaded region is 7*\pi, what is the total area, to the nearest whole number, of the unshaded regions of quadrilateral ABCD ?
Choices:
A.4
B.6
C.8
D.9
E.10
|
B
|
mathverse_vi_3838
|
|
<image>What fraction of the area of the figure is shaded?
Choices:
A.3/8
B.1/4
C.1/8
D.1/10
E.1/16
|
B
|
mathverse_vi_3843
|
|
<image>In the figure above, the area of the shaded portion is how many times the area of one of the small circles?
|
1
|
mathverse_vi_3848
|
|
<image>In the figure above, the circle has radius 7. What is the area of triangle ABC?
|
49
|
mathverse_vi_3853
|
|
<image>In the figure above, lines l and m are not parallel. Which of the following cannot be the value of x?
Choices:
A.89
B.90
C.91
D.92
E.93
|
B
|
mathverse_vi_3858
|
|
<image>In the figure above. If m = 40 and p = 25, what is the value of x?
Choices:
A.15
B.20
C.25
D.40
E.65
|
A
|
mathverse_vi_3863
|
|
<image>In the figure above, what is the value of x?
Choices:
A.72
B.70
C.68
D.66
E.64
|
A
|
mathverse_vi_3868
|
|
<image>The perimeter of the figure above is p and the area of the figure is 36. If l and w are integers, what is one possible value of p?
|
24
|
mathverse_vi_3873
|
|
<image>In the figure above, if the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?
|
50
|
mathverse_vi_3878
|
|
<image>In the figure above. If x = 80, what is the value of z?
Choices:
A.80
B.60
C.50
D.40
E.10
|
A
|
mathverse_vi_3883
|
|
<image>In the figure above. If AB = AO, what is the degree measure of angle ABO?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.90*\degree
|
D
|
mathverse_vi_3888
|
|
<image>In the figure above, if r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?
Choices:
A.45
B.50
C.65
D.75
E.It cannot be determined from the information given
|
C
|
mathverse_vi_3893
|
|
<image>In figure above, the length of AB is 3. What is the length of BC?
Choices:
A.3*\sqrt{3}
B.4*\sqrt{2}
C.4*\sqrt{3}
D.6*\sqrt{2}
E.5*\sqrt{3}
|
A
|
mathverse_vi_3898
|
|
<image>In the figure above, area of ABCE is 1. What is the perimeter of polygon ABCDE?
Choices:
A.4
B.5
C.6
D.7
E.8
|
B
|
mathverse_vi_3903
|
|
<image>In the figure above. If AE = x and ED = 4, what is length BC?
Choices:
A.6
B.8
C.2*x
D.4*x
E.4*x^2
|
B
|
mathverse_vi_3908
|
|
<image>If x = 20 and y = 30 in the figure above, what is the value of z?
Choices:
A.60
B.70
C.80
D.90
E.100
|
B
|
mathverse_vi_3913
|
|
<image>If the circumference of the large circle is 36, what is the length of the darkened arc?
Choices:
A.10
B.8
C.6
D.4
E.2
|
D
|
mathverse_vi_3918
|
|
<image>In the figure above, a shaded polygon which has equal sides is partially covered with a sheet of blank paper. If x + y = 80, how many sides does the polygon have?
Choices:
A.Ten
B.Nine
C.Eight
D.Seven
E.Six
|
B
|
mathverse_vi_3923
|
|
<image>In the figure above. If the radius of the larger circle is 4, what is the radius of the smaller circle?
Choices:
A.1
B.2
C.4
D.8
E.16
|
B
|
mathverse_vi_3928
|
|
<image>In the figure above, the smaller circles each have radius 3. What is the perimeter of the shaded region?
Choices:
A.6*\pi
B.8*\pi
C.9*\pi
D.12*\pi
E.15*\pi
|
D
|
mathverse_vi_3933
|
|
<image>If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
Choices:
A.5*a^2 + 10
B.25*a^2 + 50
C.25*a^2 + 100
D.125*a^2 + 250
E.cannot be determined
|
D
|
mathverse_vi_3938
|
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