Description:
Volume questions ask you to compute the volume of a given solid using one
of several equations found at the beginning of each math section.
Approach:
Hard questions often ask you to determine how many small volumes can be placed
into a large volume. Watch your units and these problems should be a snap.
1) Rectangular Solid
Volume = Length * Width * Height.
V = LWH
Length of diagonal:
![[Image: d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}]](http://upload.wikimedia.org/math/7/1/2/7122dc6c69436cf2ec0814ec2e397e02.png)
1-1. Practice:
-
What is the volume of a rectangular solid with the following dimensions: length = 10, height = 5, and width = 12.
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A rectangular solid has a volume of 180 cubic feet. The height is 6 feet. The width is 5 feet. What is the length?
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What is the length of the diagonal of a rectangular box that has a height of 2, a length of 4, and a width of 9?
2) Cube
![[Image: Diagram of a cube]](/MindFish/resized-image.ashx/__size/550x0/__key/CommunityServer.Wikis.Components.Files/sat_5F00_preparation/7357.cube.png)
The volume of a cube is (length of side or edge)3.
V = L3
2-1. Practice:
-
What is the volume of a cube with edges measuring 3 inches?
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What is the length of the diagonal of the cube from the previous problem?
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The volume of a cube is 1000 cubic meters. What is the length of its edges?
3) Cylinder
Volume = Pi * Radius2 * Height.
V = πr2h
2-1. Practice:
-
The radius of a cylinder is 2. Its height is 6. What is its volume?
-
A cylinder has a volume of 400π. If its height is 4, what is the measure of its radius?
-
What is the area of the circular base of the cylinder in problem 2?
4) Small Volumes Into Large Volume
Many volume questions ask you to compute how many small units will fit into a larger unit.
In order to do these questions you must find the large volume and small volume using the
same units. Finally, divide the large volume by the small volume to determine the number of
small units that can fit into the larger volume.
5) Problem:
How many cylindrical buckets with radius 5 inches and height 10 inches will it take to fill a
swimming pool with dimensions 100 feet by 15 feet by 10 feet?
![[Image: Diagram for cylinder volume problem]](/MindFish/resized-image.ashx/__size/550x0/__key/CommunityServer.Wikis.Components.Files/sat_5F00_preparation/0005.cylinder.png)
