Here are the solutions for the volume practice problems shown on the worksheet. I have calculated each one step-by-step using the standard formulas for volume.
Formulas used:
*
Cylinder: $V = \pi r^2 h$
*
Cone: $V = \frac{1}{3} \pi r^2 h$
*
Sphere: $V = \frac{4}{3} \pi r^3$
*
Hemisphere: $V = \frac{2}{3} \pi r^3$ (Half of a sphere)
* *Note: $\pi$ is approximated as $3.14$. Answers are rounded to two decimal places.*
Step-by-Step Solutions
1. Cylinder ($r=5$, $h=10$)
* Formula: $V = 3.14 \times 5^2 \times 10$
* Calculation: $3.14 \times 25 \times 10 = 785$
* Answer:
$785 \text{ cm}^3$
2. Cone ($d=6$, so $r=3$; $h=9$)
* Formula: $V = \frac{1}{3} \times 3.14 \times 3^2 \times 9$
* Calculation: $\frac{1}{3} \times 3.14 \times 9 \times 9 = 3.14 \times 27 = 84.78$
* Answer:
$84.78 \text{ in}^3$
3. Cone ($r=5$, $h=10$)
* Formula: $V = \frac{1}{3} \times 3.14 \times 5^2 \times 10$
* Calculation: $\frac{1}{3} \times 3.14 \times 25 \times 10 = \frac{785}{3} \approx 261.67$
* Answer:
$261.67 \text{ cm}^3$
4. Sphere ($r=6$)
* Formula: $V = \frac{4}{3} \times 3.14 \times 6^3$
* Calculation: $\frac{4}{3} \times 3.14 \times 216 = 4 \times 3.14 \times 72 = 904.32$
* Answer:
$904.32 \text{ yds}^3$
5. Cylinder ($d=8$, so $r=4$; $h=10$)
* Formula: $V = 3.14 \times 4^2 \times 10$
* Calculation: $3.14 \times 16 \times 10 = 502.4$
* Answer:
$502.4 \text{ ft}^3$
6. Hemisphere ($d=7$, so $r=3.5$)
* Formula: $V = \frac{2}{3} \times 3.14 \times 3.5^3$
* Calculation: $\frac{2}{3} \times 3.14 \times 42.875 \approx 89.75$
* Answer:
$89.75 \text{ ft}^3$
7. Cylinder ($r=12$, $h=20$)
* Formula: $V = 3.14 \times 12^2 \times 20$
* Calculation: $3.14 \times 144 \times 20 = 9,043.2$
* Answer:
$9,043.2 \text{ ft}^3$
8. Cylinder ($r=5$, $h=10$)
* Formula: $V = 3.14 \times 5^2 \times 10$
* Calculation: $3.14 \times 25 \times 10 = 785$
* Answer:
$785 \text{ mm}^3$
9. Sphere ($d=10$, so $r=5$)
* Formula: $V = \frac{4}{3} \times 3.14 \times 5^3$
* Calculation: $\frac{4}{3} \times 3.14 \times 125 \approx 523.33$
* Answer:
$523.33 \text{ m}^3$
10. Cylinder ($r=5$, $h=10$)
* Formula: $V = 3.14 \times 5^2 \times 10$
* Calculation: $3.14 \times 25 \times 10 = 785$
* Answer:
$785 \text{ in}^3$
11. Sphere ($r=7$)
* Formula: $V = \frac{4}{3} \times 3.14 \times 7^3$
* Calculation: $\frac{4}{3} \times 3.14 \times 343 \approx 1,436.03$
* Answer:
$1,436.03 \text{ yds}^3$
12. Cylinder ($V=380$, $r=5$; Find $h$)
* Formula rearranged: $h = V / (\pi r^2)$
* Calculation: $380 / (3.14 \times 25) = 380 / 78.5 \approx 4.84$
* Answer:
$4.84 \text{ ft}$
13. Cylinder ($d=10$, so $r=5$; $h=10$)
* Formula: $V = 3.14 \times 5^2 \times 10$
* Calculation: $3.14 \times 25 \times 10 = 785$
* Answer:
$785 \text{ in}^3$
14. Sphere ($d=8$, so $r=4$)
* Formula: $V = \frac{4}{3} \times 3.14 \times 4^3$
* Calculation: $\frac{4}{3} \times 3.14 \times 64 \approx 267.95$
* Answer:
$267.95 \text{ yds}^3$
15. Cone ($d=6$, so $r=3$; $h=20$)
* Formula: $V = \frac{1}{3} \times 3.14 \times 3^2 \times 20$
* Calculation: $\frac{1}{3} \times 3.14 \times 9 \times 20 = 3.14 \times 3 \times 20 = 188.4$
* Answer:
$188.4 \text{ ft}^3$
Final Answer:
1. 785 cm³
2. 84.78 in³
3. 261.67 cm³
4. 904.32 yds³
5. 502.4 ft³
6. 89.75 ft³
7. 9,043.2 ft³
8. 785 mm³
9. 523.33 m³
10. 785 in³
11. 1,436.03 yds³
12. 4.84 ft
13. 785 in³
14. 267.95 yds³
15. 188.4 ft³
Parent Tip: Review the logic above to help your child master the concept of volume of a cylinder cone and sphere worksheet.
