Question

the volume of a cylinder is 88 cm cube and its height is 63 cm find the curved surface area and it was surface area of the cylinder ​

Answer 1

Answer:

Step-by-step explanation: v=88

πr²h =88

r=2/3

csa=2πrh

       2x22/7x2/3x63

       264cm²

sa=2πrh+πr²h

     264+88

            352cm²

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Answer 2

Answer:-

• Curved surface area of the cylinder is 264 cm².
• Total surface area is approx 266.79 cm².

Step-by-step explanation:

Given :–

Volume of cylinder = 88cm³

Height of the cylinder = 63 cm

To Find:-

(i) Curved surface area of the cylinder

(ii) Total Surface Area of the cylinder

As we know the formula for the volume of cylinder is πr²h where 'r' is the radius of the cylinder and 'h' is the height of the cylinder.

Therefore according to the question:-

$\rightarrow \sf{ \pi {r}^{2}h = 88 {cm}^{3}} \\ \\ \rightarrow \sf{} \frac{22}{7} \times {r}^{2} \times 63 = 88 \\ \\ \rightarrow \sf{ \frac{22}{7} \times {r}^{2} = \frac{88}{63} } \\ \\ \rightarrow \sf{ {r}^{2} = \frac{ \cancel88}{ \cancel63} \times \frac{ \cancel7}{ \cancel22} } \\ \\ \rightarrow \sf{ {r}^{2} = \frac{4}{9} } \\ \\ \rightarrow \sf{r = \sqrt{ \frac{4}{9} } } \\ \\ \rightarrow \sf \boxed{\red{{r = \frac{2}{3} }}}$

Now we can find values with the help of formula

(i) Curved surface area of cylinder = 2πrh

$\rightarrow \sf{2 \times \frac{22}{7} \times \frac{2}{3} \times 63} \\ \\ \rightarrow \sf{ \frac{88}{ \cancel21} \times \cancel63} \\ \\ \rightarrow \sf{88 \times 3} \\ \\ \rightarrow \sf \boxed{ \green{{C.S.A = 264 \: {cm}^{2} }}}$

(ii) T.S.A. of cylinder = 2πr(r + h)

$\rightarrow \sf{2 \times \frac{22}{7} \times \frac{2}{3} \: (\frac{2}{3} + 63)}\\ \\ \rightarrow \sf{ \frac{88}{21} \: ( \frac{2 + 63 \times 3}{3} )} \\ \\ \rightarrow \sf{ \frac{88}{21} \: (\frac{2 + 189}{3}) } \\ \\ \rightarrow \sf{ \frac{88}{21} \times { \frac{191}{3} }} \\ \\ \rightarrow \sf{ \frac{16808}{63}} \\ \\ \rightarrow \sf \boxed{ \blue{{T.S.A. = 266.79 \: {cm}^{2} \:approx}}}$

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