A magic 8-ball has a diameter of 5 inches. It is filled 85% full with blue water. How much space is occupied by the water? Round to the nearest tenth.
Understand the Problem
The question is asking us to calculate the volume of water inside a spherical ball, given its diameter and the percentage it is filled. We will first calculate the volume of the entire sphere, and then multiply the result by the filled percentage.
Answer
$55.6$ cubic inches
Answer for screen readers
$55.6$ cubic inches
Steps to Solve
- Find the radius
The diameter of the magic 8-ball is 5 inches. The radius is half of the diameter: $r = \frac{5}{2} = 2.5$ inches
- Calculate the volume of the sphere
The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. Substitute $r = 2.5$ into the formula: $V = \frac{4}{3}\pi (2.5)^3$ $V = \frac{4}{3}\pi (15.625)$ $V = \frac{4}{3} \cdot 15.625 \cdot \pi$ $V \approx 65.45$ cubic inches
- Determine the volume of the water
The ball is filled 85% full with water. So, we need to find 85% of the total volume. Volume of water = $0.85 \times V$ Volume of water = $0.85 \times 65.45$ Volume of water $\approx 55.6325$ cubic inches
- Round to the nearest tenth
Round the volume of water to the nearest tenth: $55.6325 \approx 55.6$ cubic inches
$55.6$ cubic inches
More Information
The magic 8-ball is an interesting toy consisting of a liquid-filled ball.
Tips
- Forgetting to divide the diameter by 2 to find the radius.
- Using the incorrect formula for the volume of a sphere.
- Forgetting to multiply the volume of the sphere by the percentage filled.
- Not rounding to the nearest tenth as requested.
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