Question

The formula for the volume of a cone is v=1/3pir^2h. Find the radius, to the nearest hundredth, of a cone with a height of 3 in. and a volume of 12in.^3.Show your steps to finding the radius to receive credit.

Answer 1

Cone Volume = (π • r² • h) ÷ 3
radius^2 = (3 * Volume) / (PI * height)
radius^2 = (3 * 12) / (PI * 3)
radius^2 = (36)/ (9.4247779608)
radius^2 = 3.8197186342
radius = 1.95

Answer 2

The radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

What is radius?

Radius is the line that connects any point of the circumference of a circle to the center of that circle.

Given:

• V = 1/3(πr²h)............... Equation 1

Where:

• V = Volume of the cone
• r = radius of the cone
• h = height of the cone

Make r the subject of the equation

• r = √(3V/πh)................ Equation 2

From the question,

Given:

• V = 12 in³
• h = 3 in

Substitute these values into equation 2

• r = √[(3×12)/(3.14×3)]
• r = √(12/3.14)
• r = √(3.82)
• r = 1.95 in.

Hence, the radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

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