Spheres — Practice Quiz

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

Formulas & key concepts

Sphere Volume

$$V = \frac{4}{3}\pi r^3$$

Sphere Surface Area

$$SA = 4\pi r^2$$

Spherical Cap Volume

$$V_{cap} = \frac{1}{3}\pi h^2(3r - h)$$

Where: \(h\) = cap height

Spherical Cap Surface Area

$$SA_{cap} = 2\pi rh$$

Practice quiz

  1. What is the volume of a sphere with a radius of $3 \text{ cm}$?

    • $36\pi \text{ cm}^3$
    • $12\pi \text{ cm}^3$
    • $108\pi \text{ cm}^3$
    • $9\pi \text{ cm}^3$

    Answer: $36\pi \text{ cm}^3$

  2. Calculate the surface area of a sphere with a radius of $5 \text{ m}$.

    • $100\pi \text{ m}^2$
    • $25\pi \text{ m}^2$
    • $50\pi \text{ m}^2$
    • $125\pi \text{ m}^2$

    Answer: $100\pi \text{ m}^2$

  3. If the volume of a sphere is $288\pi \text{ cm}^3$, what is its radius?

    • $6 \text{ cm}$
    • $8 \text{ cm}$
    • $12 \text{ cm}$
    • $4 \text{ cm}$

    Answer: $6 \text{ cm}$

  4. A sphere has a surface area of $64\pi \text{ m}^2$. What is its radius?

    • $4 \text{ m}$
    • $8 \text{ m}$
    • $2 \text{ m}$
    • $16 \text{ m}$

    Answer: $4 \text{ m}$

  5. Find the volume of a spherical cap with a radius of $6 \text{ cm}$ and a height of $2 \text{ cm}$.

    • $\frac{64}{3}\pi \text{ cm}^3$
    • $16\pi \text{ cm}^3$
    • $32\pi \text{ cm}^3$
    • $48\pi \text{ cm}^3$

    Answer: $\frac{64}{3}\pi \text{ cm}^3$

  6. Calculate the surface area of a spherical cap from a sphere with radius $10 \text{ m}$ and the cap height is $3 \text{ m}$.

    • $60\pi \text{ m}^2$
    • $30\pi \text{ m}^2$
    • $100\pi \text{ m}^2$
    • $20\pi \text{ m}^2$

    Answer: $60\pi \text{ m}^2$

  7. If the radius of a sphere is doubled, how does its volume change?

    • It is multiplied by $8$
    • It is multiplied by $4$
    • It is multiplied by $2$
    • It is multiplied by $16$

    Answer: It is multiplied by $8$

  8. What is the volume of a hemisphere (a spherical cap where $h=r$) if the sphere's radius is $R$?

    • $\frac{2}{3}\pi R^3$
    • $\frac{4}{3}\pi R^3$
    • $\frac{1}{3}\pi R^3$
    • $2\pi R^2$

    Answer: $\frac{2}{3}\pi R^3$

  9. A spherical cap has a surface area of $24\pi \text{ cm}^2$ and is part of a sphere with a radius of $6 \text{ cm}$. What is the height of the cap?

    • $2 \text{ cm}$
    • $4 \text{ cm}$
    • $1 \text{ cm}$
    • $3 \text{ cm}$

    Answer: $2 \text{ cm}$

  10. For a sphere with radius $r$, what is the ratio of its surface area to its volume?

    • $\frac{3}{r}$
    • $3r$
    • $\frac{r}{3}$
    • $4\pi r$

    Answer: $\frac{3}{r}$

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