Q11 of 35 Page 74

If the ratio of length breadth and height of a cuboidal box is 3:2:1 and its volume is 384cc. then let us calculate the total surface area of the box.

Let the ratio be in x.

∴ length = 3x


breadth = 2x


and height = x


Given, volume = 384 cc


⇒ 3x × 2x × x = 384


⇒ 6x3 = 384


⇒ x3 = = 64


⇒ x = cm.


⇒ x = 4 cm


So, length = 3×4 = 12 cm


breadth = 2×4 = 8 cm


height = 4 cm


Therefore, Surface area of cuboidal box = 2(length× breadth + breadth×height + height×length)


surface area = 2(12×8 + 8×4 + 4×12)


= 2(96 + 32 + 48)


= 2×176


= 352 sq. cm.


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