Question

A toy is in the form of a cone mounted on a hemisphere with same radius

Answer 1

.. A toy is in the form a of radius 3.5 cm mounted on a hemisphere of same radius.

Answer 2

Appropriate 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 us 15.5 cm . find the total surface area of the toy .

Solution :

It is given that ,

Radius of the hemisphere ( r ) = 3.5 cm

Height of the conical part = ( 15.5 - 3.5 ) cm = 12 cm

Let , l be the slant height of the conical part . therefore ,

$\sf{}l = \sqrt{ {h}^{2} + {r}^{2} } \\ \\ \sf{}l = \sqrt{ {(12)}^{2} + {(3.5)}^{2} } \\ \\ \sf{}l = \sqrt{144 + 12 .25} \\ \\ \sf{}l = \sqrt{156.25} \\ \\ \sf{}l = 12.5 \: cm$

Therefore, slant height of the conical part is 12.5 cm in length .

Now,Total surface area of the toy = 2πr² + πrl

By substituting the values,

$\sf{}\pi \: r(2r \: + l) \\ \\ \sf{} = \frac{22}{7} \times 3.5 \times (7 + 12.5) \\ \\ = \frac{22}{7} \times 3.5 \times 15 \\ \\ \boxed{\sf{} = 214.5 {cm}^{2} }$

Therefore, total surface area of the toy is equals to 214.5 cm².

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$\underline{ \underline{ \sf{ \red{ \bold{ more \: Formulas}}}}} \\ \\ \: \sf{}volume \: of \: cube \: = {a}^{3} \\ \\ \sf{}volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \sf{}volume \: of \: cone = \frac{1}{3} \pi \: {r}^{2} h \\ \\ \sf{}volume \: of \: sphere \: = \frac{4}{3} \pi \: {r}^{3} \\ \\ \sf{} volume \: of \: hemisphere = \frac{2}{3} \pi {r}^{3}$