Chapter 11 Review

What is the volume?

• 36 cm³

• 100 cm³

• 216 m³

• None of the above

Answer explanation

V=Bh
B is area of the base. The base is a triangle.
Area of a triangle is $\frac{1}{2}bh$ .

The base of this triangle is 3 and the height is 4.
$\frac{1}{2}\cdot3\cdot4=6$ , so B = 6
What is height (h) in the volume formula? That's the height of the prism itself, which is h=6.

V=Bh
V = (6)(6)
V = $36\ cm^3$

What is the volume?

• 141.4 in³

• 231.4 in³

• 93.6 in³

• None of the above

Answer explanation

$V=\pi r^2h$
r is the radius, which is r = 3 here.
h is the height, which is h = 5 here.

$V=\pi\ \cdot\left(3\right)^2\left(5\right)$
$V=\pi\left(9\right)\left(5\right)$
$V=45\pi$
$V=141.3716694$

What is the volume?

• 21 mm³

• 42 mm³

• 17 mm³

• None of the above

Answer explanation

$V=\frac{1}{3}Bh$
B is the area off the base. This pyramid has a square base. What is the area of a square with sides 3mm long? $3^2=9$
The area is 9, so B = 9.
h is the height of the pyramid itself, which is given as h = 7.

$V=\frac{1}{3}\left(9\right)\left(7\right)$
$V=21$

Find the surface area of the prism.

• 94

• 23

• 105

• None of the above

Answer explanation

$S.A.=ph+2B$
The base here is rectangular.
The area of a rectangle is l*w.
The length of the base is 3 and the width is 5.
So the area of the base is 3*5, or B = 15.
p is the perimeter of the base (sum of all the side lengths). If the base has 2 sides that measure 3 and 2 sides that measure 5, then p = 3+3+5+5, which is p=16.
The height of the prism is h = 4.

$S.A.\ =\left(16\right)\left(4\right)+2\left(15\right)$

$S.A.=64+30$
$S.A.\ =\ 94$

Find the surface area of the cylinder in terms of pi.

• $54\pi$

• $35\pi$

• $62\pi$

• None of the above

Answer explanation

$S.A.=2\pi rh\ +\ 2\pi r^2$
We are given 6, which is the DIAMETER.
$\frac{6}{2}=3$ , so 3 is the radius, r. r = 3.

The height (h) of the entire cylinder is 6.

$S.A.=2\pi\left(3\right)\left(6\right)+2\pi\left(3\right)^2$
$S.A.=2\pi\left(18\right)+\ 2\pi\left(9\right)$
$S.A.\ =\ 36\pi+18\pi$
$S.A.\ =\ 54\pi$

Find the lateral area of the cone in terms of pi.

• $60\pi$

• $35\pi$

• $80\pi$

• None of the above

Answer explanation

$L.A.=\pi rl$
'r' is the radius, 6, so r = 6.
'l' is the slant height. We are given both the height and the slant height, but we just need 10, which is our slant height, so l = 10.

$L.A.=\pi\left(6\right)\left(10\right)$
$L.A.=60\pi$

Find the surface area of the cone in terms of pi.

• $144\pi$

• $152\pi$

• $128\pi$

• None of the above

Answer explanation

$S.A.=\pi rl\ +\ \pi r^2$
r is the radius, which is given, so r = 8.
'l' is the slant height, which is given, so l = 10.
$S.A.=\pi\left(8\right)\left(10\right)+\pi\left(8\right)^2$
$S.A.\ =\ 80\pi+64\pi$
$S.A.=144\pi$

The surface area of a sphere is  $100\pi$ .  What is its volume in terms of  $\pi$ ?

•  $\frac{500}{3}\pi$  

•  $\frac{200}{6}\pi$  

•  $\frac{700}{3}\pi$  

• None of the above

Which best compares the volumes of cylinder X and

cylinder Y?

• The volume of cylinder X is less than the volume of cylinder Y.

• The volume of cylinder X is equivalent to the volume of cylinder Y.

• The volume of cylinder X is greater than the volume of cylinder Y.

• There is not enough information to compare the volumes.

Prism J and prism K have the same volume.

What is the width w of prism K?

• 2

• 8

• 4

• 16