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Cylinder, cone and sphere
This test covers the principal elements and properties of cylinders, cones and spheres. Tasks calculate volume, lateral and total surface area, interpret axial sections and select an appropriate formula.
Questions: 10Estimated time: 20 minutes
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Question 1out of 10
A cone has radius 4 cm and height 6 cm. Using π ≈ 3.14, find volume.
Cone volume is one third of the corresponding cylinder volume: V = πr²h/3. Use π = 3.14 and cm³.
Question 2out of 10
A cylinder has radius 7 cm and height 9 cm. Using π ≈ 3.14, find volume.
Cylinder volume is circular base area × height: V = πr²h. Use π = 3.14 and cm³.
Question 3out of 10
How do surface area and volume scale when all lengths are multiplied by k?
Scaling similar solids by length factor k scales areas by k² and volumes by k³. Area depends on two length dimensions and volume on three.
Question 4out of 10
A sphere has radius 27 cm. Using π ≈ 3.14, find volume.
Sphere volume is V = 4πr³/3. Cube the radius, multiply by 4 and 3.14 and divide by 3. Use cm³.
Question 5out of 10
A cone has radius 10 cm and slant height 12 cm. Using π ≈ 3.14, find lateral area.
Cone lateral area is S = πrl, where l is the slant height. Do not add the base area πr² because only lateral area is requested.
Question 6out of 10
What shape is an axial section of a cylinder?
A cylinder axial section is a rectangle with sides 2r and h. Its area is 2rh. Use the diameter, not just the radius.
Question 7out of 10
A sphere has radius 24 cm. Using π ≈ 3.14, find volume.
Sphere volume is V = 4πr³/3. Cube the radius, multiply by 4 and 3.14 and divide by 3. Use cm³.
Question 8out of 10
A cylinder has radius 5 cm and height 3 cm. Using π ≈ 3.14, find total surface area.
A closed cylinder surface includes two bases and the curved side: S = 2πr² + 2πrh. Use π = 3.14 and cm².
Question 9out of 10
A cone has radius 2 cm and slant height 20 cm. Using π ≈ 3.14, find lateral area.
Cone lateral area is S = πrl, where l is the slant height. Do not add the base area πr² because only lateral area is requested.
Question 10out of 10
A cylinder has radius 6 cm and height 6 cm. Find axial-section area.
A cylinder axial section is a rectangle with sides 2r and h. Its area is 2rh. Use the diameter, not just the radius.
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Sample questions
- A cylinder has radius ___ cm and height ___ cm. Using π ≈ 3.14, find volume.
- A cylinder has radius ___ cm and height ___ cm. Using π ≈ 3.14, find total surface area.
- A cylinder has radius ___ cm and height ___ cm. Find axial-section area.
- A cone has radius ___ cm and height ___ cm. Using π ≈ 3.14, find volume.
- A cone has radius ___ cm and slant height ___ cm. Using π ≈ 3.14, find lateral area.
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