• 0
Newbie

# A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy.

• 0

One of the important question for the board exam class 10 from
mensuration chapter.This question is from r d sharma class 10 maths.
chapter-16.2 question number-4 maths r d sharma,mensuration.

In this question we have to find the surface area of the toy,
givwn that a toy is in the form of a cone surmounted on a hemisphere.
The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively.

Share

1. Given that,

The height of the cone (h) = 4 cm

Diameter of the cone (d) = 6 cm

So, its radius (r) = 3

Let, â€˜lâ€™ be the slant height of cone.

Then, we know that

l2 = r2 + h2

l2 = 32 + 42 = 9 + 16 = 25

l = 5 cm

Hence, the slant height of the cone (l) = 5 cm

So, the curved surface area of the cone (S1) = Ï€rl

S1 = Ï€(3)(5)

S1 = 47.1 cm2

And, the curved surface area of the hemisphere (S2) = 2Ï€r2

S2 = 2Ï€(3)2

S2 = 56.23 cm2

So, the total surface area (S) = S1 + S2

S = 47.1 + 56.23

S = 103.62 cm2

Therefore, the curved surface area of the toy is 103.62 cm2

• 0