Word problems on Volume of Cones, Cylinders, and Spheres

Volume of Cone

Volume of cone = $\frac{1}{3}\pi$ $\times$ $r^{2}$ $\times$ h, where $\pi$ = 3.14 or $\frac{22}{7}$

Example: Find the volume of a cone with radius 2 cm and height 7 cm. (Round the answer to nearest hundredth place)

Solution: Volume of cone = $\frac{1}{3}$ $\pi$ $\times$ $r^{2}$ $\times$ h= $\frac{1}{3}$ $\pi$ $\times$ $2^{2}$ $\times$ 7= $\frac{28}{3}$ $\pi$ = 29.31 cm³

Volume of Cylinder

Volume of cylinder = $\pi$ $\times$ $r^{2}$ $\times$ h, where $\pi$ = 3.14 or $\frac{22}{7}$ .

Example: Find the volume of a cylinder with diameter 4 feet and height 7 feet. (Use = $\pi$ $\frac{22}{7}$ )

Solution: Volume of cylinder = $\pi$ $\times$ $r^{2}$ $\times$ h= $\frac{22}{7}$ $\times$ $2^{2}$ $\times$ 7=22 $\times$ 4= 88 ft³

Volume of Sphere

Volume of sphere = $\frac{4}{3}$ $\pi$ $r^{3}$ , where $\pi$ = 3.14 or $\frac{22}{7}$ .

Example: Linda purchased a spherical aquarium of diameter 70 cm. What is the volume of aquarium? (Use $\pi$ = $\frac{22}{7}$ )

Volume of sphere = $\frac{4}{3}$ $\pi$ $r^{3}$ = $\frac{4}{3}$ $\times$ $\frac{22}{7}$ $\times$ $(35)^{3}$ =25666.67 cm³

Check Point

What is the capacity of a silo (silo is a large cylindrical vessel for storing bulk materials) with height 90 ft and diameter 30 ft? (Use $\pi$ = 3.14)
Find the volume of an ice cream cone with radius 5 cm and a height of 12 cm. (Use $\pi$ = 3.14)
What is the volume of water tank with a diameter of 4 feet and height 6 ft (Use $\pi$ = 3.14)
What is the volume of cone with diameter of 2 mi and a height of 12 mi? (Use $\pi$ = 3.14 and round the answer to nearest tenth)
What is the volume of a spherical ball with radius 10 cm? (Use $\pi$ = 3.14)

Answer key

63,585 ft³
314 cm³
75.36 ft³
12.6 mi³
3,140 cm³

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