Here are the step-by-step solutions for each problem on the worksheet.
1) Rectangular Prism
*
Formula: Volume = Length $\times$ Width $\times$ Height
*
Calculation: $6 \times 6 \times 12$
* $36 \times 12 = 432$
*
Answer: 432 cu yd
2) Rectangular Pyramid
*
Formula: Volume = $\frac{1}{3} \times \text{Base Area} \times \text{Height}$
*
Base Area: $4 \times 12 = 48$ sq mm
*
Calculation: $\frac{1}{3} \times 48 \times 10$
* $16 \times 10 = 160$
*
Answer: 160 cu mm
3) Square Pyramid
*
Formula: Volume = $\frac{1}{3} \times \text{Base Area} \times \text{Height}$
*
Base Area: $2 \times 2 = 4$ sq cm
*
Calculation: $\frac{1}{3} \times 4 \times 10$
* $40 \div 3 = 13.333...$
*
Answer: 13.33 cu cm
4) Cube
*
Formula: Volume = Side $\times$ Side $\times$ Side ($s^3$)
*
Calculation: $5 \times 5 \times 5$
* $25 \times 5 = 125$
*
Answer: 125 cu mm
5) Trapezoidal Prism
*
Step 1 (Area of Base): The base is a trapezoid. Formula: $\frac{(b_1 + b_2)}{2} \times h$.
* $\frac{(3 + 13)}{2} \times 7 = \frac{16}{2} \times 7 = 8 \times 7 = 56$ sq in.
*
Step 2 (Volume): Multiply Base Area by the length of the prism (height).
* $56 \times 4 = 224$
*
Answer: 224 cu in
6) Triangular Pyramid
*
Step 1 (Area of Base): The base is a right triangle with legs 12 ft and 6 ft.
* Area = $\frac{1}{2} \times 12 \times 6 = 36$ sq ft.
*
Step 2 (Volume): Multiply by height and divide by 3.
* $\frac{1}{3} \times 36 \times 13$
* $12 \times 13 = 156$
*
Answer: 156 cu ft
7) Triangular Prism
*
Step 1 (Area of Base): The base is a triangle with base 6 yd and height 4 yd.
* Area = $\frac{1}{2} \times 6 \times 4 = 12$ sq yd.
*
Step 2 (Volume): Multiply Base Area by the length of the prism (12 yd).
* $12 \times 12 = 144$
*
Answer: 144 cu yd
8) Cylinder
*
Formula: Volume = $\pi \times r^2 \times h$
*
Calculation: $\pi \times 7^2 \times 10$
* $49\pi \times 10 = 490\pi$
* $490 \times 3.14159... \approx 1539.38$
*
Answer: 1,539.38 cu ft
9) Cone
*
Formula: Volume = $\frac{1}{3} \times \pi \times r^2 \times h$
*
Calculation: $\frac{1}{3} \times \pi \times 3^2 \times 11$
* $\frac{1}{3} \times \pi \times 9 \times 11$
* $3\pi \times 11 = 33\pi$
* $33 \times 3.14159... \approx 103.67$
*
Answer: 103.67 cu in
──────────────────────────────────────
Final Answer:
1) 432 cu yd
2) 160 cu mm
3) 13.33 cu cm
4) 125 cu mm
5) 224 cu in
6) 156 cu ft
7) 144 cu yd
8) 1,539.38 cu ft
9) 103.67 cu in
Parent Tip: Review the logic above to help your child master the concept of volume of prisms and cylinders worksheet answers.
