Question

The curved surface of a cylindrical pillar is 66m^2 and its volume is 198m^3 find the height of pillar

Answer 1

Answer:-

The height of the cylindrical pillar is 1. 75m.

Explaination:-

Given:–

Curved surface area of cylinder = 66m²

Volume of the cylinder = 198m³

Now we will solve question with the help of formula's.

Also we have formula for the curved surface area of the cylinder that is 2π(rh)

where :-

r will be the circular radius and

h will be the height of the cylinder.

That's why:-

=> 2π(rh) = 66m²

=> 2 x 22/7 x (rh) = 66 m²

=> (rh) = 66 x 7/44 m

=> (rh) = 21/2 m.... Equation (1)

And we know that the volume of the cylinder is πr²h,

Therefore:-

=> πr²h = 198 m³

=> 22/7 x r² x h = 198 m³

=> r²h = 198 x 7/22 m²

=> r²h = 63 m²....... Equation (2)

On solving further using Equation (1) in Equation (2) we get,

=> r²h = r(rh)

=> 63m² = r(21/2)m

=> r = 6 m

Now on putting the value of r in the case of Equation (1), we get

=> rh = 21/12m²

=> 6h = 21/2 m²

=> h = 21/12 m

=> h = 1.75 m

Therefore:-

The height of the cylindrical pillar is 1. 75m.

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Answer 2

Answer:

• Height of cylindrical pillar = 1.75 m (Approx).

Step-by-step explanation:

Given:

• Curved surface area of cylinder pillar = 66 m²
• Volume of cylinder pillar = 198 m³

To Find:

• Height of the cylindrical pillar.

Now, we know that,

$\longrightarrow \bf Curved\;surface\;area\;of\;cylinder=2\pi rh\\ \\ \longrightarrow \sf 66\;m^{2}=2 \pi rh\;\;\;\;\;\;...............(1)\\ \\ \\ \longrightarrow \bf Volume\;of\;cylindrical\;pillar =\pi r^{2}h\\ \\ \longrightarrow \sf 198\;m^{3}=\pi r^{2}h\;\;\;\;\;..................(2)$

Now, Divide equation (2) by equation (1), we get

$\longrightarrow \sf \dfrac{\pi r^{2}h}{2\pi rh}=\dfrac{198}{66}\\ \\ \\ \longrightarrow \sf \dfrac{r}{2}= 3\\ \\ \longrightarrow \sf r = 6\;m$

Now, put the value of 'r' in equation (1), we get

$\longrightarrow \sf 2\pi rh = 66\\ \\ \longrightarrow \sf 2 \times 3.14\times 6\times h=66\\ \\ \longrightarrow \sf 37.68h=66\\ \\ \longrightarrow \sf h=\dfrac{66}{37.68}\\ \\ \longrightarrow \sf h = 1.75\;m\;(Approx)$

Hence, Height of cylindrical pillar = 1.75 m (Approx).

#answerwithquality

#BAL