Note that the solid is a rectangular prism with a hemispherical hole. To find the volume of the solid, we need to subtract the volume of the hole from the volume of the prism. Let's start by finding the volume of the prism. Recall that the volume of a rectangular prism with length l, width w, and height h can be calculated using the following formula.
V=l w hWe are given that l= 10, w= 10, and h= 13, so we have enough information to calculate the volume of the rectangular prism.
The volume of the rectangular prism is 1300 cm^3. Next, we will find the volume of the hole. Recall that the volume of a hemisphere with radius r is half the volume of a sphere with radius r.
Volume of a Hemisphere [0.8em]
V=1/2(4/3π r^3) ⇔ V=2/3π r^3
In this case, we are given that the diameter of the hemisphere is 10 centimeters. To find the radius, we need to divide the diameter by 2.
We got that the volume of the hole is about 261.8 cm^3. Finally, we can calculate the volume of the solid by subtracting the volume of the hole from the volume of the prism.
1300-261.8= 1038.2
Therefore, the volume of the solid is about 1038.2 cm^3.
