To find the volume of the composite figure, find the volume of the top and bottom figures and then add them.
C
c
Substitute the value of π for π in your answer in Part B.
A
a
Half of a cylinder and a rectangular prism
B
b
(72 π +528) in.^3
C
c
754 in.^3
Practice makes perfect
a
Let's look at the top figure first. The base is a hemisphere, which is half of a circular base. Therefore, the top figure is half of a cylinder. The bottom half of the backpack has a rectangular base. Therefore, the bottom figure is a rectangular prism.
b
To find the volume of the backpack, we will need to find the volume of the top and bottom figures separately and then take the sum. Let's start by finding the volume of the top figure using the formula for the volume of a half cylinder.
V=1/2 π r^2 h
The diameter of the cylinder is equal to the length of the rectangular base, which is 12 inches. Because the radius of a circle equals half the diameter, this implies r= 6 inches. Furthermore, the height of the cylinder is equal to the width of the rectangular base, 4 inches. Let's substitute these values to find the volume of the top figure.
The volume of the top figure is 72 π cubic inches. To find the volume of the bottom figure, we will use the formula for a prism.
V=B * h, where B is the area of the base
The base is in the shape of a rectangle. Using the formula for the area of a rectangle, the formula for volume of the prism is as follows.
V=B * h ⇔ V= ( l * w) * h
Let's start by finding the height, h. The height of the prism will be the difference between the height of the entire backpack and the radius of the cylinder.
h=Height of backpack- Radius of cylinder
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h=17- 6=11
The height of the prism is equal to 11 inches. Looking at the prism, we can see the length of the base is 12 inches and the width is 4 inches. Let's substitute these values into the formula to find the volume of the bottom figure of the backpack.
The volume of the bottom figure is 528 cubic inches. The volume of the backpack will be the sum of the volumes of the top and bottom figures.
V_(Backpack)=(72 π +528) in.^3
c
To find the volume of the backpack to the nearest cubic inch, we will multiply 72 by the value of π. Let's do it!
