Volume and Area in 7th Grade Math

Much of what 7th graders learn about volume and area is actually review. However, by the end of the school year, your child should be able to find the area of a number of 2-dimensional figures, the surface area of several 3-dimensional figures and the volume of solids.

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Studying Area and Volume in 7th Grade

Students learn a variety of different formulas in 7th grade. To review this material at home, have your 7th grader write each formula on a note card to keep in his or her backpack for quick reference. If his or her teacher requires the students to memorize certain formulas, then you can use the note cards for review. Remember that frequency and consistency are the best ways to learn a new concept, so go over the formulas every night with your child.

Area of 2-Dimensional Figures

At the beginning of the school year, students will review the formulas and methods for finding the areas of shapes with three and four sides as well as circles. Area is expressed as 'square units.' These formulas include:

Square Multiply the side of a square by itself. If each side is 5', then the area if found by multiplying 5 x 5. This is often written as A = b^2.

Rectangle Multiply the base by the height, or A = bh.

Parallelogram The formula is the same as for a rectangle: A = bh.

Trapezoid One pair of sides of a trapezoid are parallel; the other two sides are not parallel. To find the area, add the lengths of the two parallel sides and find the average by dividing by two. Multiply this by the height to find the area. The formula for this is A = (b1 + b2)/2 * h.

Triangle Multiply the base by the height and divide by two: A = (bh)/2.

Circle Multiply pi (3.14) by the radius squared: A = pi r^2.

Surface Area of 3-Dimensional Figures

Seventh graders review how to find the surface area of cubes and rectangular prisms. They also learn to calculate the surface area of cylinders. The answers should be labeled as 'square units.' They will likely find the surface area for the following shapes.

Cube Since the six sides are all the same size, you can find the area of one side (l^2) and multiply that by six: A = 6(l^2).

Rectangular prism Find the area of one side, its adjacent side and one end. Multiply each by two and add the results together. In other words, if l is the length, w the width and h the height, the formula is A = 2lw + 2wh + 2lh.

Cylinder Add the surface area of the side to two times the area of an end. Since the ends are circles, use the formula A = pi r^2 where r is the radius. The surface area of the side is the height (h) times the circumference (the formula for finding the circumference is pi times the diameter, or d). The formula may be written two different ways: A = (2 pi r^2) + (2 pi r h) or A = (2 pi r^2) + (pi d h).

Volume of 3-Dimensional Figures

Students learn to figure the volume of a number of solid shapes. This is almost all new material because only the cube and rectangular prism have been learned earlier. Volume is expressed as cubic units. Volumes that are commonly studied in 7th grade are:

Cube Multiply the length of a side by itself three times; the formula is A = l^3.

Rectangular prism Multiply the lengths of the three sides (length, width and height) with each other: A = lwh.

Triangular prism Multiply the length by the width by the height and divide the answer by two: A = lwh/2.

Cylinder Multiply the base times the height. Because the base is a circle, the formula is A = pi r^2 h.

SphereThe formula is V = (3 pi r^3)/4.

Cone Multiply the height of the cone by the area of the base and divide by three. Since the base is a circle, you find its area by using pi r^2. As a result, the formula is V = (pi r^2 h)/3.

Pyramid This is the same as finding the volume of a cone, except the base may be a triangle or a quadrilateral - usually a square or rectangle. The general formula is V = (bh)/3. Find 'b' by using the formula for either a triangle or the proper quadrilateral.

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