Question

A toy is made by mounting a cone onto a hemisphere. The radius of the cone
and a hemisphere is 7 cm. The total height of the toy is 31 cm. Find the total
surface area of the toy.

( Please explain the full answer )​

Answer 1

Answer:

858

Step-by-step explanation:

slant height = l = sqrt((24x24)+(7x7)) = 25 cm

TSA(toy) = CSA(cone) + csa(hemisphere)

= (pi x r x l) + (2 x pi x r x r)

= pi x ((r x l) + (2 x r x r))

= pi x ((7 x 25) + (2 x 7 x 7))

= pi x 273

= (22 / 7) x 273

= 858 sq. cms.

Answer 2

Let us first start by taking each part of toy and entire toy separately.

For Hemisphere part of toy :-

$R = 7 cm$

$H = R = 7 cm$

For conical part of toy :-

$R = 7 cm$

$H=31-7=24cm$               (you would see the reason below)

For the entire toy :-

$H=31cm$

What we did above was that we took the entire height of the toy and substracted the height of the hemispherical part of the toy.

Now, let us find what we require. That is, the surface area of the entire toy.

For Hemisphere part of toy :-

lateral surface area $= 2\pi r^2$

                                 $=2*3.14*7*7=307.72cm^2$

For conical part of toy :-

lateral surface area $=\pi r\sqrt{h^{2}+r^2 }$

                                $=3.14*7\sqrt{24^2+7^2}$

                                $=549.5cm^2$

For the entire toy :-

total lateral surface area = lateral surface area of cone +

                                            lateral surface area of hemisphere

                                        $=307.72+549.5=857.22cm^2$

∴ The surface area of the entire toy is 857.22 $cm^2$.