It’s a good idea to review how to use a formula. Our basic formula for finding volume of any solid figure is B x h. In this formula the B stands for the measure of the area of the base and the h stands for the height of the figure. Your first step will always be to find the area of the base of the figure. The area formulas that will be required for sixth grade volume are: rectangle (A=lw), triangle (A=lw/2) and circle (A = π r 2) . The area for a rectangle will be the first step used to solve for the volume of a rectangular prism. The area for a triangle will be used as a first step to find the volume of a triangular prism. Lastly, the area of a circle will be used to calculate the volume of a cylinder. After finding the area of the base, you simply need to multiply that figure by the height of the solid. Finally, you will write your final answer in cubic units. Since we are measuring the inside of a solid shape, it is being measured in cubic units (3-D), and the units must be shown cubed, to the third power. Here are example of how solve to find the volume for each type of figure.
Rectangular Prism - (Base l = 5 m, w = 3m) (height, h = 10m)
1. V = B x h
2. V = (l x w) x h
Step 2 Explanation: l x w is substituted in for B because this is the formula used to find the area of the base.
3. V = 5 x 3 x 10
Step 3 Explanation: substitute in the value for each variable as given in the problem.
4. V = 15 x 10
Step 4 Explanation: Solve by using the order of operations. Since both operations are multiplication you move from left to right to solve.
5. V = 150 m3
Step 5 Explanation: 15 x 10 = 150, so this is our final calculation. However, you must not forget to write in the unit (m, meters) and cube it (put it to third power).
Triangular Prism – (BASE b = 4, h = 5) (height, h = 10)
1. V = B x h
Triangular prisms can be confusing because there will be two heights. The area of triangle is measured by the base x height of that triangle. This is similar to length x width of a rectangle. The two height may be confusing, but it is important to remember that all that you’re truly asked to do to solve for volume is multiply all three amounts and then divide by two.
2. V = (b x h † 2) x h
Step 2 Explanation: The B is replaced with the area formula for a triangle.
3. V = (4x5/2) x 10
Step 3 Explanation: All variables are replaced with their values from the original problem.
4. V = (20/2) X 10
5. V = 10 x 10
6. V = 100 cm3
Steps 4 – 6 Explanation: Solve by using the order of operations, moving left to right. Don’t forget to cube your units (cm) in the final answer.
Cylinder – (BASE radius – 10 ft) (height, h = 6 ft)
1. V = B x h
2. V = (π r 2) x h
Step 2 Explanation: The B is replaced with the area formula for a circle.
3. V = (3.14 x 10 2) x 6
Step 3 Explanation: The value of each variable is substituted into the problem. The symbol π has an estimated value worth 3.14 or 22/7. This is a constant and will always be used to solve for the area of a circle. The bolded values were taken from the original problem.
4. V = (3.14 x 100) x 6
Step 4 Explanation: The order of operations requires exponents to be solved before multiplication. 10 2 is requiring the solution of an exponent. Exponents are solved by multiplying the base number,10, by itself, so 10 x 10 = 100.
5. V = 314 x 6
Step 5 Explanation: The order of operations requires all numbers within grouping symbols, parenthesis to be solved. Hence 3.14 x 100 = 3.14.
6. V = 1,884 ft3
Step 6 Explanation: Solve by using the order of operations, moving left to right. Don’t forget to cube your units (ft) in the final answer.