Question

Given a cone with a volume of 56.52 in^3 and height 7 in., find the base radius of the cone.Use 3.14 for pi. Round your answer to the tenths place. a. 2.1 in c. 4.9 in b. 2.8 in d. 4.3 in

Answer 1

Answer: c.
`4.9\ in.`

Explanation:

The volume of cone is given by :-

`V=(1)/(3)\pi r^2 h`, where r is radius and h is height of the cone.

Given: Height : 7 in.

Volume :
`56.52\ in^3`

Then the volume of the cone will be :-

`56.52=(1)/(3)(3.14) r^2(7)\\\\\Rightarrow\ r^2=(56.52*3)/(7\cdot3.14)\\\\\Rightarrow\ r^2=24.22285714\\\\\Rightarrow\ r=4.921672189\approx4.9\ in.`

Hence, the radius of the cone =
`4.9\ in.`

Answer 2

B

Explanation:

Volume of Cone formula is given by :
`V=(1)/(3)\pi r^2 h`

Given V = 56.52 and h = 7, we plug them in and solve for r:

`V=(1)/(3)\pi r^2 h\\56.52=(1)/(3)(3.14) r^2 (7)\\56.52=7.33r^2\\(56.52)/(7.33)=r^2\\7.71=r^2\\r=√(7.71)\\ r=2.77`

rounding to tenths place, r = 2.8 inches

Answer choice B is right