Question

Identify the option with the dimensions of a rectangular prism that has the same volume as that of a prism with the dimensions 3 cm, 5 cm and 8 cm.

• A. 2 cm, 6 cm, 10 cm
• B. 3 cm, 4 cm, 9 cm
• C. 5 cm, 6 cm, 8 cm
• D. 2 cm, 8 cm, 10 cm

Answer 1

The correct option is A 2 cm, 6 cm, 10 cm

Volume of a rectangular prism
= length $\times$ width $\times$ height

Volume of the rect. prism with dimensions 3 cm, 5 cm, 8 cm:
V = 3 cm $\times$ 5 cm $\times$ 8 cm = 120 cu cm

Let us now find the volume of the rectangular prisms in the options.

Vol. of a rect. prism with dimensions
5 cm, 6 cm, 8 cm:
V = 5 cm $\times$ 6 cm $\times$ 8 cm = 240 cu cm

V(2 cm, 6 cm, 10 cm)
= 2 cm $\times$ 6 cm $\times$ 10 cm
= 120 cu cm

V(2 cm, 8 cm, 10 cm)
= 2 cm $\times$ 8 cm $\times$ 10 cm
= 160 cu cm

V(3cm, 4 cm, 9 cm)
= 3 cm $\times$ 4 cm $\times$ 9 cm
= 108 cu cm

$\therefore$ The correct answer is 2 cm, 6 cm, 10 cm as the prism with these dimensions has a volume equal to that with dimensions 3 cm, 5 cm and 8 cm, which is 120 cu cm.