Kairay created a sculpture by forming a hemisphere with a radius of 20 inches and then removing a hemisphere with a radius of 15 inches from it. Calculate the volume of his sculpture. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number. (1 point)
O 19, 363in .^ 3
O 7065in .^ 3
O 16 ,747 ln.^ 3
O 9.682in .^ 3
5
To calculate the volume of Kairay's sculpture, we need to find the volume of the larger hemisphere and subtract the volume of the smaller hemisphere that was removed.
The volume of a hemisphere is given by the formula \( \frac{2}{3} \pi r^3 \), where \( r \) is the radius of the hemisphere.
Let's first calculate the volume of the larger hemisphere with a radius of 20 inches:
\( V_{large} = \frac{2}{3} \pi (20)^3 \)
Using 3.14 as an approximation for \( \pi \):
\( V_{large} = \frac{2}{3} \times 3.14 \times 20^3 \)
\( V_{large} = \frac{2}{3} \times 3.14 \times 8000 \)
\( V_{large} = \frac{2}{3} \times 25,120 \)
\( V_{large} = 16,746.6667 \) cubic inches
Now let's calculate the volume of the smaller hemisphere with a radius of 15 inches:
\( V_{small} = \frac{2}{3} \pi (15)^3 \)
Again using 3.14 as an approximation for \( \pi \):
\( V_{small} = \frac{2}{3} \times 3.14 \times 15^3 \)
\( V_{small} = \frac{2}{3} \times 3.14 \times 3375 \)
\( V_{small} = \frac{2}{3} \times 10,593.75 \)
\( V_{small} = 7,062.5 \) cubic inches
Finally, to get the volume of the sculpture:
\( V_{sculpture} = V_{large} - V_{small} \)
\( V_{sculpture} = 16,746.6667 - 7,062.5 \)
\( V_{sculpture} = 9,684.1667 \) cubic inches
Rounded to the nearest whole number:
\( V_{sculpture} \approx 9,684 \) cubic inches
The closest answer choice to our calculated volume is:
O 9,682in .^3