Question

Toy is in the form of a cone of radius 7cm mounted on a hemisphere of same radius the total height of the toy is 31 cm find the total surface area of the toy

Answer 1

______Heyy Buddy ❤________

____Here's your Answer _________

$c.s.a. \: of \: cone \: = \: \pi \: r \: l \\ \\ = > \frac{22}{7} \times 7 \times ( \sqrt{ {r}^{2} + {h}^{2} } ) \\ \\ = > 22 \times ( \sqrt{ {7}^{2} + {(31 - 7)}^{2} } \\ \\ = > 22 \times \sqrt{49 + {24}^{2} } \\ \\ = > 22 \times \sqrt{49 + 576} \\ \\ = > 22 \times \sqrt{625} \\ \\ = > 22 \times 25 \\ \\ = > 550 \: {cm}^{2}$

Now,

$c.s.a. \: o f \: hemisphere \: = 2\pi {r}^{2} \\ \\ = > 2 \times \frac{22}{7} \times {7}^{2} \\ \\ = > 2 \times 22 \times 7 \\ \\ = > 44 \times 7 \\ \\ = > 308 \: {cm}^{2}$

Now,

Total Surface Area of Toy = C.S.A. of Cone + C.S.A. of Hemisphere

=> (550 + 308) cm^2

=> 858 cm^2.
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Answer 2

$\tt{\huge{ANSWER:}}$

Given:

Radius of the cone = 7 cm
Height of the cone = 31 cm
Radius of the hemisphere = 7 cm

To find:

The Total Surface Area of the toy

To find this, we need the curved surface area of both, the cone, as well as the hemisphere.

Curved Surface Area of Cone = $\pi r l$

l = $\sqrt{h^{2} + r^{2}}$
=》 $\sqrt{(31-7)^{2} + 7^{2}}$
=》 $\sqrt{625}$
=》 25

Put the values in the formula, you get;

=》 $\pi \times 7 \times 25$

=》 $175\pi$

Now, the Curved Surface Area of the Hemisphere = $2\pi r^{2}$

Put the value in the formula, you get;

=》 $\pi \times 2 \times 7^{2}$

=》 $98\pi$

Total Surface Area of the Toy = ${175\pi + 98\pi}$

=》 ${273\pi}$

Put the value of $\pi$ which is = $\frac{22}{7}$

=》 $\frac{22}{7}\times 273$

=》 ${858\:cm^{2}}$

Hope it Helps! :)