Question

The volume of a cylinder is 2376 cu.cm .If the radius of the base of the cylinder is 6cm, then the height of the cylinder is (a) 28cm (b) 24cm (c) 21cm (d) 22cm​

Answer 1

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given :-}}}}}}$

• ➬ Volume of cylinder = 2376 cm³
• ➬ Radius of base = 6 cm

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$\large\underline{\underline{\maltese{\gray{\pmb{\sf{\: To \: Find :-}}}}}}$

• ➬ Height of cylinder = ?

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❒ Formula Used :

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{Volume{\small_{(Cylinder) }} = π r² h}}}}}$

➢Here :

• ➳ Volume = 2376 cm³
• ➳ π = pi = 22/7
• ➳ r = Radius = 6 cm
• ➳ h = Height = ?

$\qquad{━━━━━━━━━━━━━━━}$

❒ Finding the Height :

$\qquad{:\longmapsto{\sf{ Volume = π r²h}}}$

$\qquad{:\longmapsto{\sf{ 2376 = \dfrac{22}{7} \times (6)² \times h}}}$

$\qquad{:\longmapsto{\sf{ 2376 = \dfrac{22}{7} \times 36 \times h}}}$

$\qquad{:\longmapsto{\sf{ 2376 \times 7= {22} \times 36 \times h}}}$

$\qquad{:\longmapsto{\sf{ 16632= 792 \times h}}}$

$\qquad{:\longmapsto{\sf{ h = \dfrac{16632}{792} }}}$

$\qquad{:\longmapsto{\sf{ h =\cancel \dfrac{16632}{792} }}}$

$\large\qquad{\color{maroon}{:\longmapsto{\underline{\boxed{\sf{H = 21\: cm }}}}}}{\pink{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Height of the cylinder is 21 cm. ❞

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Answer 2

Solution:

Volume of a cylinder = 2376cm³

Radius of a cylinder = 6cm

Height of a cylinder = ?

$\large\tt{Volume_{[cylinder]}}=\pi{r}^{2}h$

$\tt \implies{h= \dfrac{V}{\pi{r}^{2}}}$

$\tt\implies{h =\dfrac{2376} {\dfrac{22}{7} \times 6^{2} }}$

$\tt\implies{h = \dfrac{2376}{ \dfrac{22}{7} \times 6 \times 6}}$

$\tt\implies{h = \dfrac{2376}{ \dfrac{792}{7} } }$

$\tt\implies{h = \dfrac{2376}{113.14}}$

$\tt\implies{h = \dfrac{2376 \times 100}{11314} }$

$\tt\implies \: h = \cancel{ \dfrac{237600}{11314} }$

$\tt\implies{h = \cancel{\dfrac{118800}{5657}}}$

$\tt\implies{h = 21cm}$

∴ Height of a cylinder = 21cm.

Hence, option (c) is the correct answer.

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Important Formulas

CSA of cube = 4a²

TSA of cuboid = 2(lb + bh + hl)

SA of sphere = 4πr²

CSA of cuboid = 2(l+b)h

CSA of cone = πrl

A of semicircle = 1/2 × π(r)²

A of circle = π(r)²

A of parallelogram = b×h

A of rhombus = 1/2 × d1 × d2

A of trapezium = 1/2×h(a+b)

Area sector of a circle = πr² × θ/360.

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