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The lateral area of the right circular c...

The lateral area of the right circular cone is `60pi`. If the radius of the base is 6, what is the volume of the cone

A

`96pi`

B

`108pi`

C

`120pi`

D

`184pi`

Text Solution

Verified by Experts

The correct Answer is:
A
The formula for the lateral surface area of a cone is in terms of c = circumference and l = slant height. You can use the given base radius to solve for the slant height :
Leteral area `=(1)/(2)cl = (1)/(2)(2pi r)l=`
`(1)/(2)(2pi xx 6)l = 6pi l = 60 pi`
`6l=60`
`l=10`
You can think of the slant height as the hypotenuse of a right triangle whose legs are the base radius and height of the cone.

Now you can see that the triangle is a 3-4-5 and that h = 8. Plug r = 6 and h = 8 into the volume formula :
Volume `=(1)/(3)pi r^(2)h=(1)/(3)pi(6)^(2)(8)=96pi`
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