(a) A rectangular parallelopiped has diamensions `10 cm xx 5 cm xx 2.5 cm`. Calculate (i) the radius of the sphere and (ii) the side of the cube which will have the same volume as the paralleopiped. (b) Which out of the three has miniumum surface area ?

Answer

(i) 3.1 cm (ii) 5cm (b) Sphere

Explanation

(a) Volume fo parallelopiped = volume of sphere = volume of cube ` lxxx bxxd = (4)/(3) pi r^3 = l'^3`
(i) `r = ((3lbd)/(4pi))^(1//3) = [(3xx10 xx 5xx2.5)/(4xx(22//7))]^(1//3) = 3.1 cm`
(ii) `l' = (lxx bxxd)^(1//3) = (10 xx 5xx2.5)^(1//3) = 5 cm`
(b) Surface area of parallelopiped ` =2( lxxb + d xx d + d xx l)`
`=2 [10 xx 5 + 5xx2.5 + 2.5 xx 10]`
=175 sq. cm. Surface area of sphere ` =4pi r^2 = 4xx(22)/(7) xx(3.1)^2 = 120.8 sq. cm` Surface area of cube ` = 6xx(l' xx l') = 6xx5xx5 = 150 sq. cm.`