Question

9. The C.S.A of a right circular cylinder of height 14 cm is 88 cm find the diameter of the base of the cylinder​

Answer 1

Explanation:

$\frak{Given}\begin{cases}& \sf{HCF\;of\;two\; Numbers =\frak{12}} \\ &\sf{LCM\;of\;two\;numbers=\frak{5040}} \\ &\sf{One\;of \: the \: number\;is=\frak{144}}\end{cases}$

Need to find: The other number?

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❍ Let the other required number be x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\bf{\star}\;\boxed{\textsf{\textbf{\pink{Product\;of\;two\; Numbers\;=\;LCM \times \: HCF}}}}$

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Therefore,

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$:\implies\sf x \times 144 = 12 \times 5040\\\\\\:\implies\sf x \times 144 = 60480 \\\\\\:\implies\sf x = \cancel\dfrac{60480}{144} \\\\\\:\implies{\underline{\boxed{\pink{\frak{x = 420}}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence, the other required number is {\textbf{420.}}}}}$

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$\qquad\quad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

HCF is (Highest common factor) which is the greatest factor b/w given any numbers.

LCM is (Lowest common factor) which is the least number and LCM is exactly divisible by two or more numbers.

Answer 2

Explanation:

π = 22/7

Height (h) of cylinder = 14 cm

Let the diameter of the cylinder be d.

Curved surface area of cylinder = 88 cm2

⇒ 2πrh = 88 cm2 (r is the radius of the base of the cylinder)

⇒ πdh = 88 cm2 (d = 2r)

⇒ 22/7 x d x 14cm = 88 cm2

⇒ d = 2cm

Therefore, the diameter of the base of the cylinder is 2 cm.