Question

the height of right circular cylinder is 10.5m. three times the sum of the areas of its two circular faces is twice the area of the curved surface. find the volume of the cylinder

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Answer 1

Step-by-step explanation:

Given:-

• The height of the right circular cylinder = 10.5m

• Three times the sum of the area of its two circular faces is twice the area of the curved surface area.

To Find:-

• The volume of the cylinder.

Solution:-

Height of the cylinder (h) = 10.5m

Let the radius of the cylinder be " r "

Area of the base of the cylinder = πr²

Area of the 2 bases of cylinder = 2πr²

Curved surface area of cylinder = 2πrh

According to the question:-

$\sf\implies 3(2\pi {r}^{2}) = 2(2\pi rh)$

$\sf\implies 6\pi {r}^{2} = 4\pi rh$

$\sf\implies 6r = 4h$

$\sf\implies 6r = 4 \times 10.5$

$\sf\implies r = \dfrac{42}{6}$

$\sf\implies r = 7$

$\therefore \sf \underline{\:\: \underline{\: Radius \: of \: the \: cylinder \: (r) = 7m\: }\: \: }$

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

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{22}{7} \times (7)^2 \times 10.5$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: = 22 \times 7\times 10.5$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1617m^3$

$\underline{\boxed{\therefore \textsf{\textbf{ Volume \: of \: the \: cylinder = 1617}} \bf{m}^{3} }}$

Answer 2

GIVEN THAT

• Height of cylinder=10.5m
• Three times the sum of the areas of its circular faces=Twice the CSA of cylinder

WE HAVE TO FIND

The volume of cylinder

First we write the given equation

ATQ

$\rm \bf{3(sum \: of \: area \: of \: circular \: face) = 2(area \: of \: cylinder)}$

We know

• CSA of cylinder=2πrh
• AREA OF CIRCLE =πr^2
• area of two circle=2πr^2

Here

$\rm \bf{3(2\pi {r}^{2}) } = 2(2\pi rh) \\ \rm \bf \implies 6\pi {r}^{2} = 4\pi rh \\ \implies \rm \bf \: 6r = 4h \\ \implies \rm \bf \: r = \frac{4 \times 10.5}{6} \\ \implies \rm \bf \boxed{ \bf r = 7}$

Volume of cylinder= πr^2h

$\bf \: volume \: of \: cylinder = \frac{22}{7} \times {7}^{2} \times 10.5 \\ \implies \boxed{\bf \: \: volume \: of \: cylinder =1617 {m}^{2} }$

Therefore volume of cylinder is 1617m^2