Question

the ratio of csa to tsa of a right circular cylinder is 1:3 find the volmum of the cylinder if it tsa is 1848cm"​

Answer 1

Question :-

The ratio of curved surface area to total surface area of a right circular cylinder is 1:3. Find the volume of the cylinder, if its total surface area is 1848 square cm.

$\large\underline{\sf{Solution-}}$

Let assume that

Radius of cylinder = r cm

Height of cylinder = h cm

Now, Given that,

$\rm \: CSA_{Cylinder} : TSA_{Cylinder} \: = \: 1 : 3$

We know,

Curved Surface Area and Total Surface Area of cylinder of radius r and height h is given by

$\boxed{\sf{ \: CSA_{Cylinder} \: = \: 2\pi \: rh \: }}$

and

$\boxed{\sf{ \:TSA_{Cylinder} \: = \: 2 \: \pi \: r \: (h \: + \: r) \: }}$

So, on substituting the values, we get

$\rm \: \dfrac{2\pi \: rh}{2\pi \: r(h + r)} = \dfrac{1}{3}$

$\rm \: \dfrac{h}{h + r} = \dfrac{1}{3}$

$\rm \: 3h = r + h$

$\rm \: 3h - h = r$

$\rm\implies \:r \: = \: 2h \: - - - (1)$

Further, given that

$\rm \: TSA_{Cylinder} = 1848$

$\rm \: 2\pi \: r(h + r) = 1848$

On substituting the value of r from equation (1), we get

$\rm \: 2 \times \dfrac{22}{7} \times 2h(2h + h) = 1848$

$\rm \: h(3h) = 147$

$\rm \: {h}^{2} = 49$

$\rm\implies \:h \: = \: 7 \: cm$

On substituting the value of h in equation (1), we get

$\rm \: r = 2 \times 7$

$\rm\implies \:r = 14 \: cm$

Now, we know that Volume of cylinder of radius r and height h is given by

$\boxed{\sf{ \:Volume_{Cylinder} = \pi \: {r}^{2} \: h \: }}$

So, on substituting the values of r and h, we get

$\rm \: Volume_{Cylinder} = \dfrac{22}{7} \times 14 \times 14 \times 7$

$\rm \: Volume_{Cylinder} =22\times 14 \times 14$

$\rm\implies \: Volume_{Cylinder} =4312 \: {cm}^{3}$

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More information

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

Answer 2

❐QuEsTiOn,

the ratio of csa to tsa of a right circular cylinder is 1:3 find the volmum of the cylinder if it tsa is 1848cm"

❐SoLuTiOn,

As we know that,

Curved surface Area and total surface area of cylinder of radius r and height is given by

$\tt \: CSA _{(Cylinder)}$

and

$\tt \: TSA_{(Cylinder)}$

So, on substituting the value, we get

$\tt \: \frac{2\pi \: rh}{2\pi \: r(h + + r)} = \frac{1}{3}$

$\tt\frac{h}{h + 3} = \frac{1}{3}$

$\tt3h \: = r + h$

$\tt3h - h = r \:$

$\tt \: r = 2h ----(1)$

Further Given that,

$\tt \: TSA_{(Cylinder)} = 1848$

$\tt2\pi \: r(h + r) = 1848$

On substituting the value of r from equation (1)

$\tt \: 2 \times \frac{22}{7} \times 2h(2h + h) = 1848$

$\tt \: h(3h) = 147$

$\tt \: {h}^{2} = 49$

$\tt \: h = 7cm$

On substituting the value of h in Equation (1) , we get

$\tt \: r \: = 2 \times 7$

$\tt \: r = 14cm$

Now, we know that volume of cylinder of radius r and height h is given by

$\tt \: Volume _{(Cylinder)} = \pi \: {r}^{2} h$

So, on substituting the value of r and h, we get

$\tt \: Volume _{(Cylinder)} = \frac{22}{7} \times 14 \times 14 \times 7$

$\tt \: Volume _{(Cylinder)} = 22 \times 14 \times 14$

$\tt \: Volume _{(Cylinder)} = 4312 {cm}^{3}$

❥Hope you get your AnSwEr.