A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 9cm. If a box contains 10 pieces of candy, how much chocolate does the box contain?Use 3.14 for π, and do not round your answer.
Question
A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 9cm. If a box contains 10 pieces of candy, how much chocolate does the box contain?Use 3.14 for π, and do not round your answer.
Solution
To solve this problem, we first need to find the volume of one piece of candy. The formula for the volume of a sphere is V = 4/3 * π * r^3, where r is the radius of the sphere.
Step 1: Find the radius of the sphere. The diameter is given as 9 cm, so the radius is half of that, which is 4.5 cm.
Step 2: Substitute the radius into the volume formula: V = 4/3 * π * (4.5 cm)^3 = 381.51 cubic cm.
Step 3: Multiply the volume of one piece of candy by the number of candies in the box to find the total volume of chocolate in the box. So, 381.51 cubic cm * 10 = 3815.1 cubic cm.
Therefore, the box contains 3815.1 cubic cm of chocolate.
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