Question

A bat manufacturing company made a huge bat for charity and got it signed by the World Cup-winning team.

The dimensions of the bat, which is in the form of a cuboid with a cylindrical handle at the top, are as follows:

Length = 2 m, width = 0.5 m, thickness = 0.1 m

Diameter of cylindrical part = 0.1 m

Height of cylindrical part = 0.7 m

Find the volume of wood used in the bat. Also, find the total surface area of the wooden bat.

Answer 1

Radius of cylinder = `0.1/2`

= `1/20` m

Height of cylindrical part (H) = 0.7 m

Length of cuboid (l) = 2 m

Width of cuboid (b) = 0.5 m

Thickness of cuboid (h) = 0.1 m

Volume of cylinder = πr²h

= `22/7 xx 1/20 xx 1/20 xx 0.7`

= `11/2000` m³

Volume of cuboid = 1 × b × h

= `2 xx 0.5/10 xx 0.1/10`

= `1/10` m³

Volume of bat = Volume of cuboid + Volume of cylinder

= `11/2000 + 1/10`

= `(11 + 200)/2000`

= `211/2000` m³

= 0.1055 m³

Total surface area of cuboid = 2(lb + bh + hl)

= 2(2 × 0.5 + 0.5 × 0.1 + 0.1 × 2)

= 2(1 + 0.5 + 0.2)

= 2(1.25)

= 2.50 m²

Total surface area of cylinder = 2πrh + 2πr²

= `2 xx 22/7 xx 1/20 xx 0.7 + 2 xx 22/7 xx 1/20 xx 1/20`

= `22/100 + 22/(100 xx 14)`

= `22/100(1 + 1/14)`

⇒ `22/100 xx 15/14`

= 0.236 m²

Total surface area of bat = 2.50 + 0.236

= 2.736 m²