Math, asked by souvikdas4223, 1 year ago

The C. S. A of cylindrical pillar is 264 & volume is 924m find diameter and height of pillar

Answers

Answered by NishanthKJ
1
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Answered by nehu215
1

Answer:

Diameter of the cylindrical pillar is 14 m and the height of the cylindrical pillar is 6 m.

Step-by-step explanation:

Given :-

CSA of a cylindrical pillar is 264 m² and volume is 924 m³.

To find :-

Diameter and height of the cylindrical pillar.

Solution :-

Let the radius of the cylindrical pillar be r m and the height of the cylindrical pillar be h m.

Formula used :

★{\boxed{\sf{CSA\: of\: cylinder=2\pi\:rh}}}

CSAofcylinder=2πrh

★ {\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}

Volumeofcylinder=πr

2

h

According to the 1st condition,

CSA of the cylindrical pillar is 264 m².

\begin{gathered}\to \sf \: 2\pi \: rh \: = 264 \\ \\ \to \sf \: 2 \times \dfrac{22}{7} \times rh = 264 \\ \\ \to \sf \: rh = 264 \times \dfrac{1}{2} \times \dfrac{7}{22} \\ \\ \to \sf \: rh = 42.............(i)\end{gathered}

→2πrh=264

→2×

7

22

×rh=264

→rh=264×

2

1

×

22

7

→rh=42.............(i)

According to the 2nd condition,

Volume of the cylindrical pillar is 924 m³.

\begin{gathered}\to \sf \: \pi {r}^{2} h = 924 \\ \\ \to \sf \: \dfrac{22}{7} \times rh \times r = 924 \\ \\ \to \sf \: \dfrac{22}{7} \times 42 \times r = 924 \\ \\ \to \sf \: 22 \times 6 \times r \: = 924 \\ \\ \to \sf \: 132r \: = 924 \\ \\ \to \sf \: r \: = 7\end{gathered}

→πr

2

h=924

7

22

×rh×r=924

7

22

×42×r=924

→22×6×r=924

→132r=924

→r=7

Radius of the cylindrical pillar is 7 m.

Diameter = 2×7 = 14 m.

Now put r = 7 in eq(i).

rh = 42

→ 7×h = 42

→ h = 42/7

→ h = 6

Height of the cylindrical pillar is 6 m.

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