Question

review homework: unit 3 - geometry question 37, 6.5.45 hw score: 56.9%, 33 of 58 points points: 0 of 1 question list question 23 question 24 question 25 question 26 question 27 question 28 a bowl is in the shape of a hemisphere (half a sphere) with a diameter of 11 inches. find the volume of the bowl. use 3.14 for π. the volume of the bowl is about (simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Find the radius of the hemisphere

The diameter of the hemisphere is 11 inches, so the radius \( r \) is half of the diameter.
\( r=\frac{11}{2} = 5.5 \) inches.

Step2: Recall the formula for the volume of a sphere

The volume of a sphere is given by the formula \( V_{sphere}=\frac{4}{3}\pi r^{3} \).

Step3: Find the volume of the hemisphere

Since the bowl is a hemisphere (half of a sphere), its volume \( V_{hemisphere} \) is half of the volume of the sphere. So \( V_{hemisphere}=\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3} \).

Step4: Substitute the values of \( \pi \) and \( r \) into the formula

We know that \( \pi = 3.14 \) and \( r = 5.5 \) inches.
First, calculate \( r^{3} \): \( r^{3}=(5.5)^{3}=5.5\times5.5\times5.5 = 166.375 \).
Then, substitute into the formula for the volume of the hemisphere:
\( V_{hemisphere}=\frac{2}{3}\times3.14\times166.375 \)
First, calculate \( \frac{2}{3}\times3.14=\frac{6.28}{3}\approx2.0933 \)
Then, multiply by 166.375: \( 2.0933\times166.375\approx348.45 \) (rounded to two decimal places)

Answer:

348.45 cubic inches