44.9k views
1 vote
The volume of a sphere is a function of its radius and is given by

V(r)= 4πr 3
___
​ 3
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.

1 Answer

4 votes

Final answer:

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).

User Mark Reinhold
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories