Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

We have,

Radius of the hemisphere = Radius of the cone = r = 3.5 cm and

Height of the cone = 15.5 – 3.5 = 12 cm

Also,

The slant height of the cone, `l = sqrt(h^2 + r^2)`

= `sqrt(12^2 + 3.5^2)`

= `sqrt(144 + 12.25)`

= `sqrt(156.25)`

= 12.5 cm

Now,

Total surface area of the toy = CSA of cone + CSA of hemisphere

= πrl + 2πr²

= πr(l + 2r)

= `22/7 xx 3.5 xx (12.5 + 2 xx 3.5)`

= 11 × (12.5 + 7)

= 11 × 19.5

= 214.5 cm² 

So, the total surface area of the toy is 214.5 cm².

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.

Answer 2

Height of hemisphere = r = 3.5 cm

Height of cone = 15.5 – 3.5 = 12 cm

Slant height of cone = `sqrt(r^2 + h^2)`

= `sqrt(12.25 + 144)`

= `sqrt(156.25)`

= 12.5 cm

Total surface area of the toy = CSA of cone + CSA of hemisphere

= πrl  + 2πr² 

= `22/7 xx 12.5 xx 3.5 + \cancel(2) xx 22/\cancel(7) xx \cancel(3.5) xx 3.5`

= 22 × 12.5 × 0.5 + 22 × 3.5

= `22 (12.5 xx 5/10 + 3.5)`

= `22 (12.5 xx 1/2 + 3.5)`

= 22 (6.25 + 3.5)

= 22 (9.75)

= 214.5 cm²

∴ Total surface area of the toy is 214.5 cm².