Question

The height of a right cone is 3 inches shorter than the radius. What is the height of the cone if the volume is 17 cubic inches?

a. 3.454 inches
b. 4.01 inches
c. 7.01 inches
d. 1.01 inches

Answer 1

1.03 inches

Explanation:

Volume of a come = 1/3πr²h

If the height of a right cone is 3 inches shorter than the radius, then;

h = r - 3

Substitute

V = 1/3πr²(r-3)

Given that V = 17in^3

17 = 1/3πr²(r-3)

17*3 = 3.14r²(r-3)

51/3.14 = r²(r-3)

16.242 = r²(r-3)

r² = 16.242

r = √16.242

r = 4.03

Since h = r - 3

h = 4.03 - 3

h = 1.03 inches

hence the height is 1.03 inches