The length, width and height of a rectangular solid are in the ratio o

1.	The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm3, the total surface area of the box isA. 27 cm2B. 32 cm2C. 64 cm2D. 88 cm2
Answer» Correct option is D. 88 cm² Given, Ratio of length , width and height of rectangular solid = 3 : 2 : 1 Volume of box = 48 cm³ Let length of box = 3x cm Breadth of box = 2x cm Height of box = x cm Volume of box = v = 3x \(\times\) 2x \(\times\) x = 48 = 6x³ = \(\cfrac{48}6\) = 8 = x = \(\sqrt[3]{8}\) = 2 cm Hence . length = 3x = 3 ×2 = 6 cm = breadth = 2x = 2 × 2 = 4 cm = height = x = 2 cm Total surface area of box = 2(lb + bh + hl) = 2(24 + 8 + 12) = 88 cm²

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm3, the total surface area of the box isA. 27 cm2B. 32 cm2C. 64 cm2D. 88 cm2

Answer»

Correct option is D. 88 cm²

Given,

Ratio of length , width and height of rectangular solid = 3 : 2 : 1

Volume of box = 48 cm³

Let length of box = 3x cm

Breadth of box = 2x cm

Height of box = x cm

Volume of box = v = 3x \(\times\) 2x \(\times\) x = 48

= 6x³ = \(\cfrac{48}6\) = 8

= x = \(\sqrt[3]{8}\) = 2 cm

Hence . length = 3x = 3 ×2 = 6 cm

= breadth = 2x = 2 × 2 = 4 cm

= height = x = 2 cm

Total surface area of box = 2(lb + bh + hl) = 2(24 + 8 + 12)

= 88 cm²