Mathematics
Find the volume, the total surface area and the lateral surface of a rectangular solid having :
(i) length = 8.5 m, breadth = 6.4 m and height = 50 cm.
(ii) length = 5.6 dm, breadth = 2.5 dm and height = 1 m.
Answer
(i) Given,
Length = 8.5 m
Breadth = 6.4 m
Height = 50 cm = 0.5 m.
Volume of rectangular solid = l × b × h
= 8.5 × 6.4 × 0.5
= 27.2 m3.
Total surface area of the rectangular solid = 2(lb + bh + hl)
= 2(8.5 × 6.4 + 6.4 × 0.5 + 0.5 × 8.5)
= 2(54.4 + 3.2 + 4.25)
= 2(61.85)
= 123.70 m2.
Lateral surface area of the solid = [2(l + b)h]
= [2(8.5 + 6.4) × 0.5]
= [2(14.9) × 0.5]
= 14.9 m2.
Hence, volume = 27.2 m3, TSA = 123.7 m2 and LSA = 14.9 m2.
(ii) Given,
Length = 5.6 dm
Breadth = 2.5 dm
Height = 1 m = 10 dm
Volume of rectangular solid = l × b × h
= 5.6 × 2.5 × 10
= 140 dm3.
Total surface area of the solid = 2(lb + bh + hl)
= 2(5.6 × 2.5 + 2.5 × 10 + 10 × 5.6)
= 2(14 + 25 + 56)
= 2(95)
= 190 dm2.
Lateral surface area of the solid = [2(l + b)h]
= [2(5.6 + 2.5) × 10]
= [2(8.1) × 10]
= 162 dm2.
Hence, volume = 140 dm3, TSA = 190 dm2 and LSA = 162 dm2.
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