Pyramids and Cones — Practice Quiz

A Geometry cheat sheet for Pyramids and Cones — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Pyramid Volume

$$V = \frac{1}{3}Bh$$

Where: \(B\) = base area, \(h\) = height

Cone Volume

$$V = \frac{1}{3}\pi r^2 h$$

Cone Surface Area

$$SA = \pi r^2 + \pi r l = \pi r(r + l)$$

Where: \(l\) = slant height

Cone Slant Height

$$l = \sqrt{r^2 + h^2}$$

Practice quiz

  1. A pyramid has a square base with side length $6 \text{ cm}$ and a height of $10 \text{ cm}$. What is its volume?

    • $120 \text{ cm}^3$
    • $180 \text{ cm}^3$
    • $360 \text{ cm}^3$
    • $60 \text{ cm}^3$

    Answer: $120 \text{ cm}^3$

  2. Calculate the volume of a cone with a radius of $3 \text{ m}$ and a height of $7 \text{ m}$.

    • $21\pi \text{ m}^3$
    • $63\pi \text{ m}^3$
    • $7\pi \text{ m}^3$
    • $9\pi \text{ m}^3$

    Answer: $21\pi \text{ m}^3$

  3. A cone has a radius of $5 \text{ cm}$ and a height of $12 \text{ cm}$. What is its slant height?

    • $13 \text{ cm}$
    • $17 \text{ cm}$
    • $7 \text{ cm}$
    • $144 \text{ cm}$

    Answer: $13 \text{ cm}$

  4. A cone has a radius of $4 \text{ cm}$ and a slant height of $5 \text{ cm}$. What is its total surface area?

    • $36\pi \text{ cm}^2$
    • $20\pi \text{ cm}^2$
    • $16\pi \text{ cm}^2$
    • $40\pi \text{ cm}^2$

    Answer: $36\pi \text{ cm}^2$

  5. A cone has a volume of $48\pi \text{ cm}^3$ and a radius of $6 \text{ cm}$. What is its height?

    • $4 \text{ cm}$
    • $8 \text{ cm}$
    • $12 \text{ cm}$
    • $2 \text{ cm}$

    Answer: $4 \text{ cm}$

  6. A cone has a volume of $75\pi \text{ m}^3$ and a height of $9 \text{ m}$. What is its radius?

    • $5 \text{ m}$
    • $25 \text{ m}$
    • $3 \text{ m}$
    • $9 \text{ m}$

    Answer: $5 \text{ m}$

  7. A cone has a radius of $3 \text{ cm}$ and a height of $4 \text{ cm}$. What is its total surface area?

    • $24\pi \text{ cm}^2$
    • $12\pi \text{ cm}^2$
    • $15\pi \text{ cm}^2$
    • $36\pi \text{ cm}^2$

    Answer: $24\pi \text{ cm}^2$

  8. A square pyramid has a base side length of $6 \text{ cm}$ and a height of $9 \text{ cm}$. A cone has a radius of $3 \text{ cm}$ and a height of $9 \text{ cm}$. Which statement is true about their volumes?

    • The pyramid's volume is greater than the cone's volume.
    • The cone's volume is greater than the pyramid's volume.
    • Their volumes are equal.
    • The pyramid's volume is half the cone's volume.

    Answer: The pyramid's volume is greater than the cone's volume.

  9. A pyramid has a volume of $200 \text{ m}^3$ and a square base with side length $10 \text{ m}$. What is its height?

    • $6 \text{ m}$
    • $2 \text{ m}$
    • $20 \text{ m}$
    • $10 \text{ m}$

    Answer: $6 \text{ m}$

  10. A cone has a total surface area of $96\pi \text{ cm}^2$ and a slant height of $10 \text{ cm}$. What is its radius?

    • $6 \text{ cm}$
    • $8 \text{ cm}$
    • $12 \text{ cm}$
    • $16 \text{ cm}$

    Answer: $6 \text{ cm}$

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