Grade 10 Math — Combined solids
Find the surface area and volume of a solid made by joining a cylinder, a cone or a hemisphere.
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1.A cylinder of radius 7 inches and height 10 inches has a cone of radius 7 inches and slant height 25 inches standing on top of it. Its outside is the cone's curved surface, the cylinder's curved surface and the circular base. Take π = 22/7. What is the total surface area, in square inches?
2.A solid is a cylinder of radius 7 inches and height 10 inches with a cone of radius 7 inches and height 12 inches standing on top of it. Take π = 22/7. What is the total volume of the solid, in cubic inches?
3.A solid is a cylinder of radius 7 inches and height 10 inches with a cone of radius 7 inches and height 12 inches standing on top of it. Take π = 22/7. What is the volume of the cone part, in cubic inches?
4.Sort each formula by what it measures.
Groups: A surface area · A volume
- πrl
- 1/3 πr²h
- 2πrh
- πr²h
- 4/3 πr³
- 3πr²
5.A toy is a cone standing on a hemisphere, both of radius 7 inches. The cone is 24 inches tall. What is the cone's slant height, in inches?
6.A solid is a cylinder of radius 7 inches and height 10 inches with a cone of radius 7 inches and height 12 inches standing on top of it. Take π = 22/7. What is the volume of the cylinder part, in cubic inches?
7.A cone, a hemisphere and a cylinder all have a radius of 7 inches, and the cone and the cylinder are both 7 inches tall. Which holds the most?
- a) The cone
- b) The cylinder
- c) The hemisphere
- d) They all hold the same
8.A sphere of radius 7 inches is cut exactly in half. Take π = 22/7. What is the total surface area of one hemisphere, counting its flat face, in square inches?
Answer key — Grade 10 Math — Combined solids
- 1. 1144
- 2. 2156
- 3. 616
- 4. 2πrh → A surface area; πr²h → A volume; 4/3 πr³ → A volume; πrl → A surface area; 3πr² → A surface area; 1/3 πr²h → A volume
- 5. 25
- 6. 1540
- 7. b) The cylinder
- 8. 462