Question

The volume of a sphere is a function of its radius and is given by

V(r)= 4πr 3
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where r is the radius of the sphere. a. Find the volume of a sphere whose radius is 3 in. Round to the nearest tenth of a cubic inch. b. Find the volume of a sphere whose radius is 12 cm. Round to the nearest tenth of a cubic centimeter.

Answer 1

To calculate the volume of a sphere, the formula V(r) = 4/3 π r^3 is used. For a radius of 3 inches, the volume is approximately 113.1 cubic inches, and for a radius of 12 cm, the volume is approximately 7238.2 cubic centimeters, both rounded to the nearest tenth.

Step-by-step explanation:

The volume of a sphere can be calculated using the formula V(r) = \( \frac{4}{3} \pi r^3 \), where V(r) is the volume and r is the radius of the sphere.

Part a:

For a sphere with a radius of 3 inches, the volume is:

V(3) = \( \frac{4}{3} \pi (3)^3 \) = \( \frac{4}{3} \pi \times 27 \) = \( \frac{4}{3} \times 3.1416 \times 27 \) ≈ \( 113.1 \) cubic inches (rounded to the nearest tenth).

Part b:

For a sphere with a radius of 12 cm, the volume is:

V(12) = \( \frac{4}{3} \pi (12)^3 \) = \( \frac{4}{3} \pi \times 1728 \) = \( \frac{4}{3} \times 3.1416 \times 1728 \) ≈ \( 7238.2 \) cubic centimeters (rounded to the nearest tenth).