Name_________________________________
CC Geo
HW #12
1. The surface area of a cube is 294 square feet. Find the volume of the cube.
49 = S2
SA = 6S2
294 = 6S
2
S = 7
V = S3
V = 343
3
V = 7
2. A cube has a volume of 512 cubic inches. Find the surface area of the cube.
S = 8 SA = 6S2
V = S3
512 = S
3
2
SA = 6(8)
SA = 384
3. Paul is designing a mold for a concrete block to be used in a custom
landscaping project. The block is shown in the diagram with its corresponding
dimensions and consists of two intersecting rectangular prisms. Find the
volume of mixed concrete, in cubic feet, needed to make Paul‛s custom block
Vback = 8*16*40 = 5120
Vfront = 24*24*8 = 4608
Vcombined = 8*8*16 = 1024
5120 + 4608 ­ 1024 = 8704 in3 8704/(123) = 5.03
4. What is the surface area of the following figure which is a rectangular prism with a
triangular prism resting on top? What is it's volume?
SA = (64*18 + 2(20)12) + (36*20 + 2(12)(6 3))
2,352 + 144 3
12ft
12ft
18 ft
V = (20*12*18) + (1/2)(12)(6 3)(20)
12ft
20 ft
5. If a rectangular pyramid is sliced parallel to its base, the remaining portion of
the pyramid is the frustum. Find the height of the frustum.
12 m
20 m
9 m
15 m
6 m
10
m
6. A water cup in the shape of a cone has a height of 4 inches and a maximum
diameter of 3 inches. What is the volume of the water in the cup, to the
nearest tenth of a cubic inch, when the cup is filled to half its height?
Review
7. Find the missing side lengths of the following triangle using sine, cosine,
and/or tangent. Round your answer to the nearest tenth.
x
16
62
y
2
8. Triangle A has a height of 12 in. and an area of 48in .
A similar triangle B has a height of 15. What is it's area?
9. ΔSTR ~ ΔVTU.
Find the length of VT and ST.
V
4
S
x
T
18
10
R
U
1)
5) h = 8
2)
6) V = 1.2 in3
3)
7) x = 30.1 y= 34.1
8) 75 in2
4)
9) ST = 5 VT = 9
SA = 64*18 + 2(20)12 + 36*20 + 2(12)(6 3)
2,352 + 144 3