Question

sarah is filling a glass sphere with decorative sand. the radius of the sphere is 2 inches. which is closest to the minimum amount of sand sarah needs to completely fill the glass sphere?
a 10.7 cu in.

b 25.1 cu in.

c 33.5 cu in.

d 100.5 cu in.

● c
○ d
○ b
○ a

Explanation:

Step1: Recall Sphere Volume Formula

The volume \( V \) of a sphere is given by the formula \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius of the sphere.

Step2: Substitute the Radius

Given that the radius \( r = 2 \) inches, substitute \( r = 2 \) into the formula:

$$ V = \frac{4}{3}\pi (2)^3 $$

Step3: Calculate the Volume

First, calculate \( (2)^3 = 8 \). Then:

$$ V = \frac{4}{3}\pi \times 8 = \frac{32}{3}\pi $$

Using \( \pi \approx 3.14 \), we have:

$$ V \approx \frac{32}{3} \times 3.14 \approx \frac{100.48}{3} \approx 33.5 \text{ cubic inches} $$

Answer:

C. 33.5 cu in.