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Match each cone's measures to its corresponding volume.

Match each cone's measures to its corresponding volume.-example-1
User Esdes
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2 Answers

3 votes

Answer:

base area=16π in² height=6 in ⇒ base area= πr²

16π²=π(r)²

r=4 in

v=1/3 ×π (4)²×(6)

v=32π in²

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v=1/3 π(12/2)²×5

v=1/3π(31)×5=

v=60π in³

-------------

v=1/3 π×(25×4)=

v=100π/3 in³

OAmalOHopeO

User TheFastCat
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4.3k points
4 votes

Matching of the cones to their volumes are:

1) Cone 1 Volume: V = 32π in³

2) Cone 2 Volume: V = 60π in³

3)Cone 3 Volume: V = 100π/3 in³

What is the Volume of the cone?

1) We are given:

base area = 16π in²

height = 6 in

Base is a circle and as such formula for the base area is:

Base area = πr²

Thus:

16π = πr²

r = 4 in

Formula for volume is:

V = ¹/₃ × πr²h

Thus:

V = ¹/₃ × π(4)² × (6)

V = 32π in³

2) The dimensions of the cone are:

diameter = 12 in

Thus; r = 12/2 = 6 in

Height: h = 5 in

Thus:

V = ¹/₃ × π(6)² × (5)

v = 60π in³

3) The dimensions of the cone are:

r = 5 in

Height: h = 4 in

Thus:

V = ¹/₃ × π(5)² × (4)

V = 100π/3 in³

User Clox
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4.2k points