Topics › KS3 › Geometry & measures

Volume of prisms

1. vol-01 Present from here

   What is the volume of this cuboid?

   
   A Option A: $10\text{ cm}^3$

   B Option B: $62\text{ cm}^3$

   C Option C: $15\text{ cm}^3$

   D Option D: $30\text{ cm}^3$
   Answer and misconceptions

   A Option A: $10\text{ cm}^3$ ✗

   Adds the dimensionsCalculates 5 + 3 + 2 instead of multiplying.

   B Option B: $62\text{ cm}^3$ ✗

   Calculates the surface area insteadFinds 2(5×3 + 5×2 + 3×2) = 62, confusing volume with surface area.

   C Option C: $15\text{ cm}^3$ ✗

   Multiplies only two dimensionsCalculates 5 × 3, the area of one face, and forgets the third dimension.

   D Option D: $30\text{ cm}^3$ ✓ Correct
2. vol-02 Present from here

   What is the volume of this triangular prism?

   
   A Option A: $240\text{ cm}^3$

   B Option B: $120\text{ cm}^3$

   C Option C: $20\text{ cm}^3$

   D Option D: $12\text{ cm}^3$
   Answer and misconceptions

   A Option A: $240\text{ cm}^3$ ✗

   Forgets to halve for the triangleCalculates 6 × 4 × 10, the volume of a cuboid.

   B Option B: $120\text{ cm}^3$ ✓ Correct

   C Option C: $20\text{ cm}^3$ ✗

   Adds the dimensionsCalculates 6 + 4 + 10 instead of multiplying.

   D Option D: $12\text{ cm}^3$ ✗

   Gives the cross-section area onlyFinds ½ × 6 × 4 = 12 but does not multiply by the length.
3. vol-03 Present from here

   The end face of this prism has area $15\text{ cm}^2$. What is the volume of the prism?

   
   A Option A: $23\text{ cm}^3$

   B Option B: $60\text{ cm}^3$

   C Option C: $120\text{ cm}^3$

   D Option D: $40\text{ cm}^3$
   Answer and misconceptions

   A Option A: $23\text{ cm}^3$ ✗

   Adds the area and the lengthCalculates 15 + 8 instead of 15 × 8.

   B Option B: $60\text{ cm}^3$ ✗

   Always halves, as for a triangular prismCalculates ½ × 15 × 8, applying the triangle ½ to every prism.

   C Option C: $120\text{ cm}^3$ ✓ Correct

   D Option D: $40\text{ cm}^3$ ✗

   Divides by 3, as for a pyramidCalculates ⅓ × 15 × 8, using the pyramid formula.
4. vol-04 Present from here

   What is the volume of this cylinder, in terms of $\pi$?

   
   A Option A: $45\pi\text{ cm}^3$

   B Option B: $15\pi\text{ cm}^3$

   C Option C: $30\pi\text{ cm}^3$

   D Option D: $180\pi\text{ cm}^3$
   Answer and misconceptions

   A Option A: $45\pi\text{ cm}^3$ ✓ Correct

   B Option B: $15\pi\text{ cm}^3$ ✗

   Forgets to square the radiusCalculates π × 3 × 5 instead of π × 3² × 5.

   C Option C: $30\pi\text{ cm}^3$ ✗

   Uses the circumference instead of the areaCalculates 2π × 3 × 5, which is the curved surface area.

   D Option D: $180\pi\text{ cm}^3$ ✗

   Uses the diameter as the radiusCalculates π × 6² × 5, doubling the radius first.
5. vol-05 Present from here

   How many $\text{cm}^3$ are in $1\text{ m}^3$?

   A Option A: $100$

   B Option B: $1\,000\,000$

   C Option C: $10\,000$

   D Option D: $1000$
   Answer and misconceptions

   A Option A: $100$ ✗

   Uses the length conversion for volumeMultiplies by 100 once, as for m to cm; it must be 100 × 100 × 100.

   B Option B: $1\,000\,000$ ✓ Correct

   C Option C: $10\,000$ ✗

   Uses the area conversion for volumeUses 100², which converts m² to cm², not m³ to cm³.

   D Option D: $1000$ ✗

   Mixes up with litres in 1 m³1 m³ is 1000 litres; each litre is a further 1000 cm³.