5th Grade Math: Area and Volume Problems

Area and volume become more complicated in 5th grade and require multiple equations. If your child needs extra practice, you can create your own problems at home using the guidelines below.

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How Can I Create 5th Grade Area And Volume Problems?

Children often further their study of surface area and volume in 5th grade math. They have to learn several new formulas and need to complete a lot of practice problems in order to commit the formulas to long-term memory. Most 5th grade surface area and volume problems involve rectangles, rectangular prisms, cubes and spheres, but some 5th grade classes may explore other shapes.

When you're creating 5th grade area and volume problems, give your child a diagram and write the dimensions on the sides. He or she can then plug the dimensions into the formulas when solving the problems. Later on, you can stop drawing the figures. Simply give them the dimensions and have your child draw his or her own figures.

Problems by Concept

Surface Area

1. Calculate the surface area of a cube whose sides are four inches long.

Surface area can be challenging because it requires students to think 3-dimensionally. To figure out surface area, you have to calculate the area of each side. For this problem, all the sides are the same length because it is a cube. In addition, there are six different surfaces: top, bottom, front, back, left and right. As a result, SA = 6 (l^2) = 6 (4^2) = 96 sq. in.

2. A rectangular prism has a width (w) of two meters, a base (b) of three meters and a height (h) of four meters.

The equation used to find the surface area of a rectangular prism is SA = 2wh + 2hb + 2wb. Rectangular prisms also have six sides, but because the sides are different sizes, the sides have to be calculated separately. The answer to this problem is 16 + 24 + 12 = 52 sq. m.

3. A sphere has a radius of 3 centimeters. What is the surface area?

The equation for the surface area of a sphere is SA = 4(pi) (r^2). For this problem, the answer is approximately 113 sq. cm.


1. Find the volume of a cube whose sides are 5 m long.

The equation for the volume of a cube is V = x^3. Because all the dimensions are the same for a cube, the calculations are simple. For this problem, V = 5^3 = 125 cubic meters.

2. A swimming pool is ten feet long, seven feet deep and eight feet wide. What is the volume of the pool?

This swimming pool is shaped like a rectangular prism. The equation used to calculate the volume of a rectangular prism is V = lwh. Therefore, the volume of this pool is V = (10) (8) (7) = 560 cubic feet.

3. A basketball has a radius of six inches. What is the basketball's volume?

A basketball is a sphere, and the volume of a sphere is calculated using this equation: V = (4/3) (pi) (r^3). As a result, the volume of this sphere is V = (4/3) (3.14) (6^3) = 904.3 cubic inches.

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