Question

please answer this question ​

Answer 1

Question

From a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.

Answer

Given :

Side of the cubical piece of wood = 21cm.

Diameter of hemisphere = 21cm.

To find :

The surface area and volume of the remaining piece.

Solution :

$\bigstar$ Surface area of remaining piece = total surface area of the cube - area of the top of the hemisphere part + curved surface area of the hemisphere.

We know that,

TSA of cube = 6a²

CSA of the hemisphere = 2πr²

Area of the top of the hemisphere part is circular is shape so, Area of circle = πr²

Now, Surface area of remaining piece,

$\sf = 6 {a}^{2} - \pi {r}^{2} + 2\pi {r}^{2}$

$\sf = 6 {a}^{2} + \pi {r}^{2}$

$\sf = 6 {(21)}^{2} + \dfrac{22}{7} \times 10.5 \times 10.5$

$\sf = (6 \times 441) + (22 \times 1.5 \times 10.5)$

$\sf = 2646 + 346.5$

$\sf = 2992.5 \: {cm}^{2}$

Thus, the Surface area of remaining piece is 2992.5 cm².

$\bigstar$ Volume of the remaining piece = volume of the cube - volume of the hemisphere.

we know that,

volume of cube = a³

Volume of hemisphere = 2/3πr³

Now, Volume of the remaining piece

$\sf = {a}^{3} - \dfrac{2}{3} \pi {r}^{3}$

$\sf = {21}^{3} - \dfrac{2}{3} \times \dfrac{22}{7} \times 10.5 \times 10.5 \times 10.5$

$\sf = 9261 - 2425.5$

$\sf = 6835.5 \: {cm}^{3}$

Thus, Volume of the remaining piece is 6835.5 cm³.

Know more :

$\dashrightarrow \sf LSA \: of \: cube = 4a^2$

$\dashrightarrow \sf Diagonal \: of \: cube = \sqrt{3a}$

$\dashrightarrow \sf TSA \: of \: hemisphere = 3πr^2$

Answer 2

Answer:

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im

serious mate wtf do you want?