A cone with a radius of 3" has a total area of 24 sq. in. Find the volume of the cone.

Solution:

Given: radius of the cone = 3 in

The total Surface area of the cone = 24 sq.in

We know that the volume of the cone is 1/ 3 πr²h.

We will first find the height of the cone using the total area.

Total Surface area = Area of the circular base + area of the curved surface

TSA = πrl + π r²

24 - 9 π = πrl

πrl = 15π [Area of the remaining curved surface]

π (3) l = 15π

Divide both sides by 3π.

l = 5.

l² = h² + r²

h= 25 - 9

h² = 16

h = 4

Using the value of h in the volume of cone 1/ 3 πr²h.

Volume = 1/ 3 × 22/ 7 × 9 × 4

= 264/ 7

= 37.71 in³

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A cone with a radius of 3" has a total area of 24 sq. in. Find the volume of the cone.

Summary:

The volume of the cone with a radius of 3 in has a total area of 24 sq. in is 37.71 in^3.