Question

the sum and height of the radius of the base of the solid cylinder is 37metre . If the total surface area of the cylinder be 1628metre square, find its volume​

Answer 1

$\large{\bf{\underline{\underline{GIVEN:-}}}}$

• Sum of radius and height of solid cylinder is (r + h) = 37m.
• T.S.A = 1628m².

$\large{\bf{\underline{\underline{TO \ FIND:-}}}}$

• Volume of cylinder.

$\large{\bf{\underline{\underline{SOLUTION:-}}}}$

We know that:

$\clubsuit \ \boxed{\sf{\blue{T.S.A=2 \times \pi \times r(r+h)}}}$

Substituting (r + h) = 37, and T.S.A as 1628,

$\sf \implies 1628=2 \times \dfrac{22}{7} \times r \times (37)$

$\sf \implies r=\dfrac{(1628 \times 7)}{(2 \times 22 \times 37)}$

$\sf \implies r=\dfrac{(\cancel{1628} \times 7)}{(\cancel{1628})}$

$\sf \implies r=7 m. \bigstar$

And, r + h = 37.

⇒ 7 + h = 37.

⇒ h = 30m. ★

$\green \bigstar$______________$\green \bigstar$

Now, volume of cylinder is given by:

$\clubsuit \ \boxed{\sf{\blue{Volume=\pi \times r^2 \times h}}}$

$\sf \implies \dfrac{22}{7} \times 7 \times 7 \times 30$

$\implies \sf{\purple{4620 m^3}}$

Answer:

Volume is 4620m³.

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Answer 2

$\huge{\blue{\underline{\underline{Answer:-}}}}$

Given:

Sum of height and radius of base of solid cylinder (h+r) is 37 m

Total surface area of cylinder is 1628 m²

To find:

Volume of cylinder = ?

Solution:

TSA = Total surface area

$\\ \\ Total \: surface \: area \: of \: cylinder \\ = 2\pi \: r {}^{2} h \\ \\ = 2\pi \: r(r + h)$

$\\ TSA = 2\pi \: r(r + h) \\ \\ 1628 = 2\pi \: r(37) \\ \\ \dfrac{1628}{2\pi \: \times 37} = r \\ \\ \frac{1628}{2 \times \frac{22}{7} \times 37 } = r$

$\\ \\ r = \dfrac{1628 \times 7}{2 \times 22 \times 37} \\ \\r = 7 \: metre$

As it is given, h+r = 37m, so by solving

$\\ h + r = 37 \\ \\ h + 7 = 37 \\ \\ h = 37 - 7 \\ \\ h = 30 \: metre$

$\\ \\ volume \: of \: cylinder \: = \pi \: r {}^{2} h \\ \\ = \dfrac{22}{7} \times (7) {}^{2} \times 30 \\ \\ = \dfrac{22}{7} \times 7 \times 7 \times 30 \\ \\ = 22 \times 7 \times 30$

$\\ \\ = 4620 \: m {}^{3}$

Required answer:

Thus, the volume of cylinder is 4620 cubic metre

Knowledge booster:

# Value of π = 22/7 or 3.14

# Try to arrange formula accordingly so that solving become easy

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