To answer the questions, we'll use the formula for the volume of a sphere, which is:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.
Question 1
Given: Radius = 7 cm
\[ V = \frac{4}{3} \times 3.14 \times (7)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 343 \] \[ V = \frac{4}{3} \times 1077.32 \approx 1436.03 \text{ cm}^3 \]
Answer: 1,436.03 cm³
Question 2
Given: Diameter = 18 inches, so radius \( r = \frac{18}{2} = 9 \) inches
\[ V = \frac{4}{3} \times 3.14 \times (9)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 729 \] \[ V = \frac{4}{3} \times 2290.26 \approx 3052.1 \text{ in}^3 \]
Answer: 3,052.1 inches³
Question 3
Given: Radius = 5 feet
\[ V = \frac{4}{3} \times 3.14 \times (5)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 125 \] \[ V = \frac{4}{3} \times 392.5 \approx 523.3 \text{ ft}^3 \]
Answer: 523.3 ft³
Question 4
Given: Diameter = 8 inches, so radius \( r = \frac{8}{2} = 4 \) inches
\[ V = \frac{4}{3} \times 3.14 \times (4)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 64 \] \[ V = \frac{4}{3} \times 200.96 \approx 268 \text{ in}^3 \]
Answer: 268 inches³
Question 5
Given: Radius = 3 cm
\[ V = \frac{4}{3} \times 3.14 \times (3)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 27 \] \[ V = \frac{4}{3} \times 84.78 \approx 113.0 \text{ cm}^3 \]
Answer: 113.0 cm³
This should cover all the questions and their respective calculations!