Question

volume and surface area of three - dimensional shapes
a sphere has a radius of 7.5 centimeters (cm).
question:
to the nearest cubic centimeter, what is the volume of the sphere?
230
1,325
1,760
14,130
$v = \frac{4}{3}\pi r^3$
$v = \frac{4}{3}(3.14)(7.5)^3$
$v = 1766$

Explanation:

Step1: Recall the volume formula for a sphere

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

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 7.5 \) cm. Using \( \pi \approx 3.14 \), we substitute these values into the formula:

$$ V = \frac{4}{3} \times 3.14 \times (7.5)^3 $$

Step3: Calculate \( (7.5)^3 \)

First, calculate \( 7.5^3 = 7.5 \times 7.5 \times 7.5 = 421.875 \).

Step4: Multiply the values

Now, substitute \( 421.875 \) back into the formula:

$$ V = \frac{4}{3} \times 3.14 \times 421.875 $$

First, calculate \( \frac{4}{3} \times 3.14 \approx 4.1867 \). Then, multiply by \( 421.875 \):

$$ 4.1867 \times 421.875 \approx 1766.25 $$

Step5: Round to the nearest cubic centimeter

Rounding \( 1766.25 \) to the nearest whole number gives \( 1766 \). Looking at the provided options, \( 1760 \) is the closest (likely due to possible rounding differences in the calculation steps or the use of a slightly different approximation for \( \pi \)).

Answer:

1,760