Question

a solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy. (Use pi=22/7 and root 149=12.2)​

Answer 1

$\huge{\text{\underline{Solution:-}}}$

★ To find:-

• Volume of toy = Volume of cone + Volume of hemisphere

★ Given:-

• Radius = 7cm
• Height of cone = 10cm

★ Volume of the cone = ⅓πr²h

$\implies$ ⅓ x 22/7 x 7 x 7 x 10

$\implies$1540 / 3 cm³

★ Volume of hemisphere = ⅔ πr³

$\implies$ ⅔ x 22 / 7 x 7 x 7 x 7

$\implies$ 2156 / 3 cm³

★ Volume of the toy = 2156/3 + 1540/3

$\implies$ 3696 / 3

$\implies{\tt{\boxed{1232 cm^3}}}$

$\implies$l² = r² + h²

$\implies$(7)² + (10)²

$\implies$49 + 100

$\implies{\tt{\boxed{149}}}$

$\implies$l = √149

$\implies{\tt{\boxed{l = 12.2cm}}}$

Area of coloured paper required = C.S.A of cone + C.S.A of hemisphere

★ C.S.A of cone = πrl

$\implies$22 / 7 x 7 x 12.2

$\implies{\tt{\boxed{268.4cm^2}}}$

★ C.S.A of hemispher = 2πr²

$\implies$ 2 x 22 / 7 x 7 x 7

$\implies{\tt{\boxed{308 cm^2}}}$

★ Area of required paper:-

$\implies$ 268.4 + 308

$\implies{\tt{\boxed{576.4cm^2}}}$

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Answer 2

$\huge\mathfrak\blue{Answer:-}$

Given:

The height of the cone is (h) = 10cm

The radius of the base is (r) = 7cm

To Find:

The volume of the toy and the area of the coloured sheet required to cover the toy.

Solution:

We know that the volume of the cone of height h and radius r is given by

V = (1/3)Пr²h

Putting the respective values, we get,

V = (1/3)П(7)²(10) cm³

= 490П/3 cm³

The volume of the hemisphere of radius

7cm is given by

V' = (2/3)Пr³

= (2/3)П(7)³

= 686П/3 cm³

Total volume = V + V'

= (490П/3 + 686П/3) cm³

= 392П cm³

= (392*22/7) cm³

= 1232 cm³

Let the slant height be l cm

l = √(r²+h²)

= √(7²+10²)

= 12.2cm

So, curved surface area of the cone  Пrl

Putting the respective values, we get

Curved Surface Area=  П(7)(12.2) cm²

= 85.4П cm²

Curved Surface Area of hemisphere = 2Пr²  cm²

= 2П(7)²  cm²

= 98П cm²

Total area = (85.4+98)П cm²

= 183.4П cm²

= (183.4*22/7) cm²

= 576.4 cm²

Therefore, the area of the coloured sheet required to cover the toy is 576.4 cm².