Question

The following geometrical shapes are made up of paper. ___ required the least amount of paper and ___ has the maximum volume.

• A. Cube, Cylinder
• B. Cylinder, Cube
• C. Cuboid, Cube
• D. Cuboid, Cylinder

Answer 1

The correct option is A

Cube, Cylinder

Calculating Surface Area of each figure:-

Surface Area of Cube = 6$a^2$= 6 $\times$ 4 $\times$ 4 = 96 $c{m}^2$

Surface Area of Cuboid = 2(lb + bh + hl) = 2(10 $\times$ 5 + 5 $\times$ 2 + 2 $\times$ 10) = 2 $\times$ 80 =160 $c{m}^2$

Surface Area of Cylinder = 2πrh = 2 $\times$ $\frac{22}{7}$ $\times$ 5 $\times$ 14 = 440 $c{m}^2$.

Hence on comparison cube would require the least amount of paper since it has the minimum surface area.

Calculating Volume of each figure :-

Volume of Cube = $a^3$ = 64 $c{m}^3$

Volume of Cuboid = l $\times$ b $\times$ h = 10 $\times$ 5 $\times$ 2 =100 $c{m}^3$

Volume of Cylinder = π$r^2$h = $\frac{22}{7}$ $\times$ 25 $\times$ 14 = 1100 $c{m}^3$

Hence on comparison cylinder would have maximum volume.