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Question
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
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Solution 1
(i)
Edge of the given cube = 8 cm
Volume of the given cube = (Edge)3 = (8)3 = 8 x 8 x 8 = 512 cm3
Total surface area of a cube = 6(Edge)2 = 6 x (8)2 = 384 cm2
(ii)
Edge of the given cube = 2 m 40 cm = 2.40 m
Volume of a cube = (Edge)3
Volume of the given cube = (2.40)3 = 2.40 x 2.40 x 2.40 = 13.824 m2
Total surface area of the given cube = 6 x 2.4 x 2.4 = 34.56 m2
Solution 2
Formulae for a Cube:
Volume (V): V = a3
Total Surface Area (TSA): TSA = 6a2
(i) Edge length = 8 cm
Volume: V = a3 = 83 = 512 cm3
Total Surface Area: TSA = 6a2 = 6 × 82 = 6 × 64 = 384 cm2
(ii) Edge length = 2 m 40 cm
Convert 2 m 40 cm to centimeters:
2 m = 200 cm, so, 2 m 40 cm = 200 + 40 = 240 cm.
Volume: V = a3 = 2403 = 240 × 240 × 240 = 13,824,000 cm3
Convert to cubic meters:
1 m3 = 1,000,000 cm3 `=>V = (1,38,24,000)/(10,00,000) = 13.224 m^3`
Total Surface Area:
TSA = 6a2 = 6 × 2402 = 6 × 57,600 = 345,600 cm2
Convert to square meters:
`1 m^2 = 10000 cm^2 => TSA = 345600/10000 = 34.56 m^2`
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