Word problems on Volume of Cones, Cylinders, and Spheres

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Volume of Cone

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

volume of cones cylinders and spheres

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}\timesh=\frac{1}{3}\pi\times2^{2}\times7=\frac{28}{3}\pi= 29.31 cm3

Volume of Cylinder

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

volume of cones cylinders and spheres

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}\timesh=\frac{22}{7}\times2^{2}\times7=22\times4= 88 ft3

Volume of Sphere

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

volume of cones cylinders and spheres

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

  1. 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)
  2. Find the volume of an ice cream cone with radius 5 cm and a height of 12 cm. (Use \pi = 3.14)
  3. What is the volume of water tank with a diameter of 4 feet and height 6 ft (Use \pi = 3.14)
  4. 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)
  5. What is the volume of a spherical ball with radius 10 cm? (Use \pi = 3.14)
Answer key
  1. 63,585 ft3
  2. 314 cm3
  3. 75.36 ft3
  4. 12.6 mi3
  5. 3,140 cm3

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