Here are the step-by-step solutions for each problem on the assignment.
1) Cylinder Volume
*
Formula: $V = \pi r^2 h$
* The radius ($r$) is 9 km and the height ($h$) is 7 km.
* $V = \pi \times 9^2 \times 7$
* $V = \pi \times 81 \times 7$
* $V = 567\pi$
* $V \approx 1781.28$
* Rounding to the nearest tenth:
1,781.3 km³
2) Cylinder Volume
*
Formula: $V = \pi r^2 h$
* The radius ($r$) is 3 and the height (length) is 15.
* $V = \pi \times 3^2 \times 15$
* $V = \pi \times 9 \times 15$
* $V = 135\pi$
* $V \approx 424.11$
* Rounding to the nearest tenth:
424.1
3) Trapezoidal Prism Volume
*
Formula: $V = \text{Area of Base} \times \text{Height of Prism}$
* First, find the area of the trapezoid base. The parallel sides are 5 and 10, and the height of the trapezoid is 4.
* $\text{Area} = \frac{1}{2}(b_1 + b_2)h = \frac{1}{2}(5 + 10)(4)$
* $\text{Area} = \frac{1}{2}(15)(4) = 30$
* Now multiply by the length of the prism (7).
* $V = 30 \times 7 = 210$
* Answer:
210
4) Rectangular Prism Volume
*
Formula: $V = l \times w \times h$
* Length = 7 cm, Width = 4 cm, Height = 8 cm.
* $V = 7 \times 4 \times 8$
* $V = 28 \times 8$
* $V = 224$
* Answer:
224 cm³
5) Triangular Prism Volume
*
Formula: $V = \text{Area of Base} \times \text{Length}$
* The base is a right triangle with legs 6 and 8.
* $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24$
* The length of the prism is 10.
* $V = 24 \times 10 = 240$
* Answer:
240
6) Cylinder Volume
*
Formula: $V = \pi r^2 h$
* The diameter is 30, so the radius ($r$) is 15. The height ($h$) is 25.
* $V = \pi \times 15^2 \times 25$
* $V = \pi \times 225 \times 25$
* $V = 5625\pi$
* $V \approx 17671.45$
* Rounding to the nearest tenth:
17,671.5
7) Mulch Word Problem
* This asks for the volume of the truck bed (a rectangular prism).
* Dimensions: 7 feet, 9 feet, and 3 feet.
* $V = 7 \times 9 \times 3$
* $V = 63 \times 3$
* $V = 189$
* Answer:
189 cubic feet
8) Find the Missing Length
*
Formula: $V = l \times w \times h$
* We know Volume = 576, Width = 12, and Height = 6. We need to find Length ($l$).
* $576 = l \times 12 \times 6$
* $576 = l \times 72$
* Divide both sides by 72: $l = \frac{576}{72}$
* $l = 8$
* Answer:
8 cm
Final Answer:
1) 1,781.3 km³
2) 424.1
3) 210
4) 224 cm³
5) 240
6) 17,671.5
7) 189 cubic feet
8) 8 cm
Parent Tip: Review the logic above to help your child master the concept of volume of prisms and cylinders worksheet answers.
