Question

If the CSA of a cylinder is 3168 sqcm and it's height is 21cm than its diameter is?​

Answer 1

$\;\;\underline{\textbf{\textsf{Given:-}}}$

• CSA of the cylinder = 3168 cm²

• Height of the cylinder = 21 cm

$\;\;\underline{\textbf{\textsf{To Find:-}}}$

• The diameter of the cylinder

$\;\;\underline{\textbf{\textsf{Solution :-}}}$

$\underline{\:\textsf{ As we know that :}}$

• CSA of the cylinder = 2πrh

$\underline{\:\textsf{ Now, put the given values in the formula :}}$

$\longrightarrow$ 3168 = 2 × $\sf{\dfrac{22}{7}}$ × r × 21

$\longrightarrow$ 3168 = 2 × 22 × r × 3

$\longrightarrow$ 3168 = 132r

$:\implies$ r = $\sf{\dfrac{3168}{132}}$

$\bf{ \longrightarrow r = 24\:cm}$

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• Diameter = 2 r

$\underline{\:\textsf{ Putting the given values in the formula :}}$

$\longrightarrow$ Diameter = 2 × 24

$\bf{ \longrightarrow Diameter = 48\: cm}$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The radius of the cylinder is \textbf{24cm }}}.$

$\underline{\textsf{ The diameter of the cylinder is \textbf{48cm }}}.$

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$\;\;\underline{\textbf{\textsf{Know More:-}}}$

•Volume of cylinder = πr²h

•T.S.A of cylinder = 2πrh + 2πr²

•Volume of cone = ⅓ πr²h

•C.S.A of cone = πrl

•T.S.A of cone = πrl + πr²

•Volume of cuboid = l × b × h

•C.S.A of cuboid = 2(l + b)h

•T.S.A of cuboid = 2(lb + bh + lh)

•C.S.A of cube = 4a²

•T.S.A of cube = 6a²

•Volume of cube = a³

•Volume of sphere = 4/3πr³

•Surface area of sphere = 4πr²

•Volume of hemisphere = ⅔ πr³

•C.S.A of hemisphere = 2πr²

•T.S.A of hemisphere = 3πr²

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Answer 2

Key Point:-

Curved surface area of cylinder = 2πrh

where, r = radius of cylinder

h = height of cylinder

Solution:-

CSA of cylinder = 3168 sq cm

height = 21 cm

CSA of cylinder = 2πrh

or, 3168 = 2×(22/7)×r×21

or, r = (3168×7)/44×21

or, r = 24 cm

Hence, Diameter of a cylinder = 2r = 48 cm...