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Katie approximated the volume and the surface area for a ball she was using for some exercises by assuming the ball is a sphere. She was surprised when the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. What is the radius of the ball?

Answer :

Answer:

3

Step-by-step explanation:

Volume of sphere:

4/3 * pi * r^3

Surface Area of Sphere:

4 * pi * r^2

So if V = SA

4/3 * pi * r^3 = 4 * pi * r^2

4/3 * pi * r^3 = 4 * pi * r^2

1/3 * r^3 = r^2

1/3 * r = 1

r = 3

Volume is a three-dimensional scalar quantity. The radius of the ball is equal to 3 units.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the sphere is given by the formula,

V = (4/3)Ļ€RĀ³

The surface area of the sphere is given by the formula,

Surface area = 4Ļ€RĀ²

Also, it is mentioned that the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. Therefore,

(4/3)Ļ€RĀ³ = 4Ļ€RĀ²

RĀ³/3 = RĀ²

R = 3

Hence, the radius of the ball is equal to 3 units.

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