#33. You are a plumber who needs to install a hollow spherical float in a water tank. You need to know the volume of the float to know how much water will be displaced by the sphere. You know that the diameter of the sphere is 8 inches. What is the volume of the sphere?

Question

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A
150.72 in.³

B
267.94 in.³

C
357.24 in.³

D
624.75 in.³

E
1,205.76 in.³

Answer 1

To calculate the volume of a sphere, you can use the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where \( V \) is the volume and \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 8 inches, you first need to find the radius:

\[ r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ inches} \]

Now, substitute the radius into the volume formula:

\[ V = \frac{4}{3} \pi (4)^3 \]

Calculating \( 4^3 \):

\[ 4^3 = 64 \]

So the volume becomes:

\[ V = \frac{4}{3} \pi \cdot 64 = \frac{256}{3} \pi \]

Using the approximate value of \( \pi \approx 3.14 \):

\[ V \approx \frac{256}{3} \cdot 3.14 \approx \frac{256 \cdot 3.14}{3} \approx \frac{804.44}{3} \approx 268.15 \text{ in.}^3 \]

Thus, the closest answer choice is:

B. 267.94 in.³