Question

The volume of a right circular cylinder is 448π cm² and height 7 cm. Find the lateral surface area
and total surface area of the cylinder.


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Answer 1

Step-by-step explanation:

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Answer 2

Given:-

• Volume of a right circular cylinder = 448π cm³
• Height of the cylinder = 7 cm

To Find:-

• Lateral Surface Area of the cylinder
• Total Surface Area of the cylinder

Solution:-

We know,

Volume of the cylinder = πr²h cu.units

Therefore,

$\sf{448\pi = \pi r^2 h}$

= $\sf{\dfrac{448\pi}{\pi} = r^2\times 7}$

= $\sf{\dfrac{448}{7} =r^2}$

= $\sf{64 = r^2}$

=> $\sf{r = \sqrt{64}}$

=> $\sf{r = 8\:cm}$

Now,

Lateral Surface Area of the cylinder = 2πrh sq.units

= $\sf{LSA = 2\times \dfrac{22}{7}\times8\times 7}$

= $\sf{LSA = 2\times 22\times 8}$

= $\sf{LSA = 352\:cm^2}$

And,

Total Surface Area of cylinder = 2πr(r + h) sq.units

$\sf{TSA = 2\times \dfrac{22}{7}\times 8(8+7)}$

= $\sf{TSA =\dfrac{352}{7}\times 15}$

= $\sf{TSA = \dfrac{5280}{7}}$

= $\sf{TSA = 754.3\:cm^2}$

Hence,

Total Surface Area of the cylinder = 754.3 cm²

Lateral Surface Area of the cylinder = 352 cm².

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Formulas used:-

• Total Surface area of the cylinder = 2πr(r + h) sq.uints
• Lateral Surface area of the cylinder = 2πrh sq.units
• Volume of the cylinder = πr²h cu.units.

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