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MathematicsGrade 8en

🎁 Surface Area & Volume of 3D Objects

Master the calculation of surface area and volume for cylinders, cones, and spheres. This quiz challenges you to apply formulas in real-world contexts, interpret scaling effects, analyze net diagrams, and solve composite shape problems. Strengthen your spatial reasoning and understanding of how these geometric measures relate to capacity, material usage, and practical design. **What you'll learn:** - Apply surface area and volume formulas accurately to cylinders, cones, and spheres - Interpret and solve real-world problems involving capacity and material requirements - Understand how scaling affects surface area and volume relationships - Analyze net diagrams and composite 3D shapes to find total surface area and volume

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Questions in this quiz

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  1. Question 1

    A cylinder has a radius of 5 cm and a height of 12 cm. What is its total surface area, including both circular bases?

  2. Question 2

    A cone has a radius of 6 cm and a slant height of 10 cm. What is its lateral surface area (curved surface only)?

  3. Question 3

    If a sphere's radius is doubled, its volume increases by a factor of 8.

  4. Question 4

    A cylindrical water tank has a radius of 2 m and a height of 5 m. Approximately how many cubic meters of water can it hold?

  5. Question 5

    A cone has a height of 9 cm and a radius of 4 cm. What is its volume?

  6. Question 6

    The surface area of a sphere with radius 5 cm is 100π100\pi cm².

  7. Question 7

    A composite shape consists of a cylinder (radius 3 cm, height 8 cm) topped with a cone (same radius, height 6 cm). What is the total volume?

  8. Question 8

    A sphere has a volume of 288π288\pi cm³. What is its radius?

  9. Question 9

    If you double the radius of a cylinder while keeping the height constant, the surface area also doubles.

  10. Question 10

    A net diagram shows a cylinder 'unfolded' into a rectangle and two circles. If the rectangle has dimensions 10 cm by 8 cm, and the circles each have a radius of 4 cm, what is the total surface area represented by this net?

  11. Question 11

    A cylindrical soup can has an outer radius of 4 cm and a height of 15 cm. The manufacturer wants to create a paper label that wraps around the lateral surface. What is the minimum length and width of the label needed?

  12. Question 12

    A cone and a cylinder with the same radius and height will have volumes in the ratio 1:3.

  13. Question 13

    Two spheres have radii in the ratio 2:3. What is the ratio of their surface areas?

  14. Question 14

    A cone is formed by rolling up a sector of a circle. The sector has a radius of 10 cm and a central angle of 144°. What is the radius of the base of the cone?

  15. Question 15

    A cone is formed by rolling up a sector of a circle with radius 10 cm and central angle 72°. What is the radius of the base of the cone?

  16. Question 16

    A cone with height 8 cm and base radius 6 cm will have the same volume as a sphere with radius 4 cm.

  17. Question 17

    A designer needs to manufacture a spherical ball with a diameter of 20 cm. The material costs $0.50 per cm². Approximately how much will the material cost?

  18. Question 18

    A cylindrical pipe has an inner radius of 3 cm, an outer radius of 4 cm, and a length of 50 cm. What is the volume of material used in the pipe?

  19. Question 19

    The total surface area of a cone includes both its lateral surface and its circular base.

  20. Question 20

    A sphere has a surface area of 576π576\pi cm². What is its volume?