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Questions and Answers
What is the volume of the smaller cylinder with a radius of 3 cm and the same height of 14 cm?
What is the volume of the smaller cylinder with a radius of 3 cm and the same height of 14 cm?
- 84.78 cm³
- 94 cm³
- 126 cm³ (correct)
- 84 cm³
What is the volume of the larger cylinder with a radius of 7 cm and height of 14 cm?
What is the volume of the larger cylinder with a radius of 7 cm and height of 14 cm?
- 1540 cm³ (correct)
- 1470 cm³
- 616 cm³
- 324 cm³
What is the formula to calculate the volume of the remaining solid after carving out the smaller cylinder from the larger one?
What is the formula to calculate the volume of the remaining solid after carving out the smaller cylinder from the larger one?
- Volume of remaining solid = Volume of larger cylinder - Volume of smaller cylinder (correct)
- Volume of remaining solid = Volume of larger cylinder × Volume of smaller cylinder
- Volume of remaining solid = Volume of smaller cylinder - Volume of larger cylinder
- Volume of remaining solid = Volume of smaller cylinder + Volume of larger cylinder
After calculating the volumes, what is the volume of the remaining solid when the smaller cylinder is removed from the larger one?
After calculating the volumes, what is the volume of the remaining solid when the smaller cylinder is removed from the larger one?
Considering both cylinders have the same height, how does height affect the volume of a cylinder?
Considering both cylinders have the same height, how does height affect the volume of a cylinder?
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Study Notes
Problem Setup
- We have two cylinders: a larger one and a smaller one carved out of it.
- Both cylinders have the same height of 14 cm.
- The larger cylinder has a radius of 7 cm.
- The smaller cylinder has a radius of 3 cm.
Finding the Volume
- We need to find the volume of the remaining solid.
- This is achieved by subtracting the volume of the smaller cylinder from the volume of the larger cylinder.
Calculating Volumes
- Volume of a cylinder: π * r^2 * h, where 'r' is the radius and 'h' is the height.
- Volume of the larger cylinder: π * 7^2 * 14 = 686π cm^3
- Volume of the smaller cylinder: π * 3^2 * 14 = 126π cm^3
- Volume of the remaining solid: 686Ï€ - 126Ï€ = 560Ï€ cm^3
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