Compute the volume and surface area of rectangular prisms of measurements given below:

(i) length 24 centimetres, breadth 15 centimetres, height 32 centimetres

(ii) length 42.5 centimetres, breadth 25 centimetres, height 86 centimetres

(iii) length 37 centimetres, breadth 23 centimetres, height 58 centimetres

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Solution

(i)

Length (l) of the rectangular prism = 24 cm

Breadth (b) of the rectangular prism = 15 cm

Height (h) of the rectangular prism = 32 cm

Volume of the rectangular prism = l × b × h

= 24 cm × 15 cm × 32 cm

= 11520 cm³

Surface area of the rectangular prism = 2(lb + bh + hl)

= 2(24 × 15 + 15 × 32 + 32 × 24) cm²

= 2(360 + 480 + 768) cm²

= 2 × 1608 cm²

= 3216 cm²

(ii)

Length (l) of the rectangular prism = 42.5 cm

Breadth (b) of the rectangular prism = 25 cm

Height (h) of the rectangular prism = 86 cm

Volume of the rectangular prism = l × b × h

= 42.5 cm × 25 cm × 86 cm

= 91375 cm³

Surface area of the rectangular prism = 2(lb + bh + hl)

= 2(42.5 × 25 + 25 × 86 + 86 × 42.5) cm²

= 2(1062.5 + 2150 + 3655) cm²

= 2 × 6867.5 cm²

= 13735 cm²

(iii)

Length (l) of the rectangular prism = 37 cm

Breadth (b) of the rectangular prism = 23 cm

Height (h) of the rectangular prism = 58 cm

Volume of the rectangular prism = l × b × h

= 37 cm × 23 cm × 58 cm

= 49358 cm³

Surface area of the rectangular prism = 2(lb + bh + hl)

= 2(37× 23 + 23 × 58 + 58 × 37) cm²

= 2(851 + 1334 + 2146) cm²

= 2 × 4331 cm²

= 8662 cm²

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