Question

On the day of her examination, Riya sharpened her pencil from both ends as shown below:

The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.

Answer 1

d = 4.2 mm   ...(Given)

r = `d/2`

= 2.1 mm

Height of cylinder = 105.6 − 2 × 2.8

= 105.6 − 5.6

= 100 mm

Height of cone = 2.8 m

`l = sqrt((2.1)^2 + (2.8)^2)`

= `sqrt(4.41 + 7.84)`

= `sqrt12.25`

= `sqrt((35 xx 35)/100)`

= `35/10`

= 3.5 mm

Total surface area = 2πrH + 2(πrl)

= 2πr(H + l)

= `2 xx 22/7 xx 2.1(100 + 3.5)`

= 44 × 0.3 × 103.5

= 1366.2 mm²