Question

find the radius of the right circular cylinder whose height is 100 m and volume is 554400 cu. m.​

Answer 1

$\sf{\underline{\underline{ \purple{ \large{Given:}}}}}$

✰ Height = 100 m

✰ Volume of a right circular cylinder = 554400 m³

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \large{To \: Find:}}}}}$

✠ Radius of the cylinder

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \large{Solution:}}}}}$

Using formula,

Volume of the cylinder = $\sf{\pi r^2 h}$

Where,

Take $\pi$ = 22/7

r = radius

h = height

Substituting the values,

⟶ 554400 = 22/7 × r² × 100

⟶ 554400 × 7/22 × 1/00 = r²

⟶ 5544 × 7/22 = r²

⟶ 1764 = r²

⟶ 42 cm = r

$\\ \\ \sf {\large {Therefore, \: radius = {\green{ \underline{ \boxed{ \sf{42 \: cm}}}}}}}$

Additional points:

• Area of circle = πr²

• Volume of cylinder = πr²h

• Total surface area of cylinder = 2πrh + 2πr²

• Total surface area of cone = πrl + πr²h

• Curved surface area of cone = πrl

• Volume of cone = 1/3 πr²h

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Answer 2

Question :-

• Find the radius of the right circular cylinder whose height is 100 m and volume is 554400 m³.

Given :-

• Volume of Cylinder = 554400m³
• Height of the Cylinder = 100m

To Find :-

• What is the Radius of the Cylinder ?

Solution :-

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

${:} \longrightarrow \sf{\sf{ \: 554400 \: = \: \dfrac{22}{7} \: \times \:r^{2} \: \times \: 100 }}$

${:} \longrightarrow \sf{\sf{ \: \dfrac{5544 \cancel{00}}{1\cancel{00}} \: = \: \dfrac{22}{7} \: \times \:r^{2} \: }}$

${:} \longrightarrow \sf{\sf{ \: 5544 \: = \: \dfrac{22}{7} \: \times \:r^{2} \: }}$

${:} \longrightarrow \sf{\sf{ \: \dfrac{5544 \: \times \: 7}{22} \: = \: l \:r^{2} \: }}$

${:} \longrightarrow \sf{\sf{ \: \dfrac{38808}{22} \: = \: \:r^{2} \: }}$

${:} \longrightarrow \sf{\sf{ \: 1764 \: = \: \:r^{2} \: }}$

${:} \longrightarrow \sf{\sf{ \: \sqrt{1764}\: = \: \:r }}$

${:} \longrightarrow \sf{\bf{ \: 42 \: = \: \:Radius }}$

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Verification :-

$\longmapsto \sf{\sf{ \: Volume\:of\: cylinder=\pi\:r^{2}h }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: \dfrac{22}{7} \: \times \: (42)^{2} \: \times \: 100 }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: \dfrac{22}{7} \: \times \: 42 \: \times \: 42 \: \times \: 100 }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: \dfrac{22}{\cancel7} \: \times \: \cancel{42} \: \times \: 42 \: \times \: 100 }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: 22 \: \times \: 6 \: \times \: 42 \: \times \: 100 }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: 132 \: \times \: 4200 }}$

$\longmapsto \sf{\sf{ \: 554400 \: = \: 554400 }}$

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So, the Radius of the Cylinder is 42cm

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★ Additional Info :-

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• L.S.A of Cylinder = 2π r h

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