Here are the step-by-step solutions to find the volume for each figure.
Helpful Formulas:
*
Cone: $V = \frac{1}{3} \pi r^2 h$ (One-third times pi times radius squared times height)
*
Sphere: $V = \frac{4}{3} \pi r^3$ (Four-thirds times pi times radius cubed)
*
Cylinder: $V = \pi r^2 h$ (Pi times radius squared times height)
* *Note: If you are given diameter ($d$), divide by 2 to get the radius ($r$).*
* *We will use $\pi \approx 3.14$.*
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1. Cone
* Radius ($r$) = 21 ft, Height ($h$) = 35 ft
* $V = \frac{1}{3} \times 3.14 \times (21)^2 \times 35$
* $21^2 = 441$
* $V = \frac{1}{3} \times 3.14 \times 441 \times 35$
* $V = 16,167.9$ cubic feet
2. Sphere
* Radius ($r$) = 6 in
* $V = \frac{4}{3} \times 3.14 \times (6)^3$
* $6^3 = 216$
* $V = \frac{4}{3} \times 3.14 \times 216$
* $V = 904.32$ cubic inches
3. Cylinder
* Radius ($r$) = 4 cm, Height ($h$) = 15 cm
* $V = 3.14 \times (4)^2 \times 15$
* $4^2 = 16$
* $V = 3.14 \times 16 \times 15$
* $V = 753.6$ cubic centimeters
4. Cylinder
* Radius ($r$) = 19 m, Height ($h$) = 9 m
* $V = 3.14 \times (19)^2 \times 9$
* $19^2 = 361$
* $V = 3.14 \times 361 \times 9$
* $V = 10,205.46$ cubic meters
5. Cone
* Radius ($r$) = 24 in, Height ($h$) = 50 in
* $V = \frac{1}{3} \times 3.14 \times (24)^2 \times 50$
* $24^2 = 576$
* $V = \frac{1}{3} \times 3.14 \times 576 \times 50$
* $V = 30,144$ cubic inches
6. Sphere
* Radius ($r$) = 3 mm
* $V = \frac{4}{3} \times 3.14 \times (3)^3$
* $3^3 = 27$
* $V = \frac{4}{3} \times 3.14 \times 27$
* $V = 113.04$ cubic millimeters
7. Sphere
* Diameter ($d$) = 12 cm, so Radius ($r$) = 6 cm
* $V = \frac{4}{3} \times 3.14 \times (6)^3$
* $6^3 = 216$
* $V = \frac{4}{3} \times 3.14 \times 216$
* $V = 904.32$ cubic centimeters
8. Cylinder
* Radius ($r$) = 8 ft, Height ($h$) = 6 ft
* $V = 3.14 \times (8)^2 \times 6$
* $8^2 = 64$
* $V = 3.14 \times 64 \times 6$
* $V = 1,205.76$ cubic feet
9. Cone
* Radius ($r$) = 3 cm, Height ($h$) = 6 cm
* $V = \frac{1}{3} \times 3.14 \times (3)^2 \times 6$
* $3^2 = 9$
* $V = \frac{1}{3} \times 3.14 \times 9 \times 6$
* $V = 56.52$ cubic centimeters
10. Cone
* Diameter ($d$) = 30 m, so Radius ($r$) = 15 m. Height ($h$) = 29 m
* $V = \frac{1}{3} \times 3.14 \times (15)^2 \times 29$
* $15^2 = 225$
* $V = \frac{1}{3} \times 3.14 \times 225 \times 29$
* $V = 6,829.5$ cubic meters
11. Cylinder
* Diameter ($d$) = 20 cm, so Radius ($r$) = 10 cm. Height ($h$) = 10 cm
* $V = 3.14 \times (10)^2 \times 10$
* $10^2 = 100$
* $V = 3.14 \times 100 \times 10$
* $V = 3,140$ cubic centimeters
12. Sphere
* Diameter ($d$) = 20 cm, so Radius ($r$) = 10 cm
* $V = \frac{4}{3} \times 3.14 \times (10)^3$
* $10^3 = 1,000$
* $V = \frac{4}{3} \times 3.14 \times 1,000$
* $V \approx 4,186.67$ cubic centimeters
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Final Answer:
1. 16,167.9 ft³
2. 904.32 in³
3. 753.6 cm³
4. 10,205.46 m³
5. 30,144 in³
6. 113.04 mm³
7. 904.32 cm³
8. 1,205.76 ft³
9. 56.52 cm³
10. 6,829.5 m³
11. 3,140 cm³
12. 4,186.67 cm³
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder and cones worksheet.
