Question

The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone? 6 = one-third pi (r squared) (8 pi) 8 pi = one-third pi (r) (6 squared) 6 = one-third (pi r)(8 pi) 8 pi = one-third pi (r squared) (6)

Answer 1

GIVEN :

The volume of a cone with a height of 6cm is $8\pi$ cubic centimeters.

a) 6 = one-third pi (r squared) (8 pi)

b) 8 pi = one-third pi (r) (6 squared)

c) 6 = one-third (pi r)(8 pi)

d) 8 pi = one-third pi (r squared) (6)

TO FIND :

The expression for the radius (r) of the base of the cone.

SOLUTION :

Given that the volume of a cone with a height of 6 cm is $8\pi$ cubic centimeters

⇒ Height (h)=6 cm and $V=8\pi$ cubic centimeters

The formula for volume of cone is given by :

$V=\frac{1}{3}\pi r^2h$ cubic units

Since $V=8\pi$ cubic centimeters and h=6 cm we have that

$8\pi=\frac{1}{3}\pi r^2(6)$ cubic centimeters.

Hence option d) 8 pi = one-third pi (r squared) (6) is correct.

ie., the expression can be used to find r is $8\pi=\frac{1}{3}\pi r^2(6)$ cubic centimeters.