A triangular prism has a base with area 45 cm² and height 14 cm. If 10% of the prism is hollowed out for wiring, what is the volume of the solid part?

Correct — A. Volume of a prism = base area × height.

Full prism = 45 × 14 = 630 cm³
Hollowed part = 10% of 630 = 63 cm³
Solid part = 630 − 63 = 567 cm³ → option (a).

Check: 90% of 630 = 0.9 × 630 = 567.

Why the others are wrong

• (b)
  594 cm³ — 594 cm³ leaves only 630 − 594 = 36 cm³ removed, about 5.7% of the prism. Ten per cent of 630 is 63, so the solid part is 567.
• (c)
  576 cm³ — 576 cm³ leaves 630 − 576 = 54 cm³ removed, about 8.6%, not 10%. It is 567 with its last two digits swapped.
• (d)
  630 cm³ — 630 cm³ is the whole prism before any of it is hollowed out. The question asks for the solid part, so the 10% must come off.

Every right prism, whatever the shape of its base, has volume = base area × height. The base area is given, so no triangle formula is needed: 45 × 14 = 630 cm³.

Removing 10% of the volume leaves 90% of it, so the solid part is 0.9 × 630 = 567 cm³.

The shape of the hollow does not matter here. The fraction removed does.

Key facts

• Volume of a right prism = base area × height.
• Here 45 cm² × 14 cm = 630 cm³.
• Keeping 90% of 630 cm³ leaves 567 cm³.

Common traps

• Halving 45 × 14 as if the base still needed ½ × base × height. 45 cm² is already the area of the triangle.
• Stopping at 630 cm³, which is on offer, and forgetting to remove the hollowed 10%.

No directly related past PYQ was found.