Getting into Solids: Pyramids - ETA hand2mind

Name __________________________________________
21 in.
8 in.
9 in.
9 in.
GETTING INTO SOLIDS — PRISMS
Worksheet 16: Answer Key
Volume
Challenge
Find the volume of the cylinder if the two cones do not
contain any substance. Describe your process through a
series of clearly shown mathematical steps.
Step 1: I will find the volume of the two right cones. You will need to reference the first book entitled,
Getting Into Solids — Pyramids.
First, I will find the area of the
base, B, of the cone, which is
a circle.
B = π r 2
B = π (8) 2
B = 64 π
Second, I will find the volume of
the right cone using the formula
V = 1 / 3 B h
V = 1 / 3 (64 π)(9)
V = 192 π
Third, since the two right cones are the same, I will double the volume to find the total volume of
both cones.
V of both cones = 192 π(2)
V of both cones = 384 π
Step 2: I will find the volume of the right cylinder.
Note: Since the base of the right Now I will find the volume of the
cylinder is exactly the same as the right cylinder using the formula,
base of the right cones, the area V = B h
of the bases will be the same. V = 64π (21)
Therefore, B = 64 π
V = 1,344 π
Step 3: I will find the volume of the solid by subtracting the volume of the two right cones from the
volume of the right cylinder.
V = volume of the cylinder - volume of the 2 cones
V = 1,344 π - 384 π
V = 960 π in. 3 3,015.93 in. 3
960 π in. 3 (or)
Solution: ______________________________
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