Questions: How much ice cream is in a spherical scoop of ice cream with a radius of 3 cm ? Use 3.14 as an approximation for pi. Round your answer to the nearest whole number. (1 point)
Transcript text: How much ice cream is in a spherical scoop of ice cream with a radius of 3 cm ? Use 3.14 as an approximation for pi. Round your answer to the nearest whole number. (1 point)
Solution
Solution Steps
Step 1: Identify the formula for the volume of a sphere
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.
Step 2: Substitute the given values into the formula
Given:
Radius \( r = 3 \, \text{cm} \)
Approximation for \( \pi = 3.14 \)
Substitute these values into the formula:
\[
V = \frac{4}{3} \times 3.14 \times (3)^3
\]
Step 3: Calculate the volume
First, calculate \( (3)^3 \):
\[
(3)^3 = 27
\]
Now, substitute this back into the equation:
\[
V = \frac{4}{3} \times 3.14 \times 27
\]
Calculate the multiplication:
\[
V = \frac{4}{3} \times 84.78
\]
\[
V = 113.04 \, \text{cm}^3
\]
Step 4: Round the answer to the nearest whole number
The volume \( 113.04 \, \text{cm}^3 \) rounded to the nearest whole number is \( 113 \, \text{cm}^3 \).