Cones, Cylinders, & Spheres Online Practice

Question

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Question
Find the volume of a sphere with a diameter of 3.5 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

43.96 ft.3
43.96 feet cubed

67.31 ft.3
67.31 feet cubed

179.05 ft.3
179.05 feet cubed

22.44 ft.3

Answer 1

To find 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.

First, you need to determine the radius from the diameter. The radius is half of the diameter. Given that the diameter is 3.5 ft, the radius \( r \) will be:

\[ r = \frac{3.5}{2} = 1.75 \text{ ft} \]

Now, substituting the radius into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times (1.75)^3 \]

Calculating \( (1.75)^3 \):

\[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375 \]

Now, substituting this back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 5.359375 \]

Calculating \( \frac{4}{3} \times 3.14 \):

\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]

Now, multiplying by \( 5.359375 \):

\[ V \approx 4.18667 \times 5.359375 \approx 22.43 \text{ ft}^3 \]

Rounding to the nearest hundredth, the volume is approximately \( 22.44 \text{ ft}^3 \).

The correct response is:

22.44 ft.³