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Vsevolod [243]
2 years ago
12

Find the volume of a cone with base area 367 ft2 and a height equal to twice the radius. a

Mathematics
1 answer:
Lostsunrise [7]2 years ago
6 0

Answer:

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Step-by-step explanation:

The formula of the volume of a cone is V =  π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

The area of the base of the cone is 36π ft²

Equate the formula of the area of the circle by 36π to find r

πr² = 36π

Divide both sides by π

r² = 36

Take √ to both sides

r = 6 ft

The height of the cone is equal to twice the radius

The radius of the cone is 6 ft

Multiply 6 by 2 to find the height

h = 2(6) = 12 ft

The height of the cone is 12 ft

Subsitute the values of h and r in the formula of the volume of the cone to find it

V =  π(6)²(12)

V = 144 π ft³

V = 452.3893421 ft³

Round it to the nearest tenth

V = 452.4 ft³

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