Question

10. The radius and height of a cylinder are in the ratio 7: 2. If the volume of the cylinder is
8316 cm", find the total surface area of the cylinder.
11. The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is
110 cm. Find the volume of the cylinder.


Guys can u plz tell me these 2 question's answer ...............​

Answer 1

Solutions:-

10. Given:-

• Ratio of radius and height of the cylinder = 7:2
• Volume of the cylinder = 8316 cm²

To find:-

Total Surface Area (TSA) of the cylinder.

Assumption:-

Let the ratio constant be x

Radius = 7x

Base = 2x

Solution:-

We know,

$\sf{Volume\:of\:cylinder = \pi r^2h\:\:cu.units}$

Therefore,

= $\sf{8316 = \dfrac{22}{7}\times(7x)^2\times2x}$

= $\sf{\dfrac{8316\times7}{22} = 49x^2\times2x}$

= $\sf{378\times7 = 98x^3}$

= $\sf{x^3 = \dfrac{378\times7}{98}}$

= $\sf{x^3 = \dfrac{2646}{98}}$

= $\sf{x^3 = 27}$

= $\sf{x = \sqrt[3]{27}}$

= $\sf{x = 3}$

Therefore,

Radius of the cylinder = 7x = 7×3 = 21 cm

Height of the cylinder = 2x = 2×3 = 6 cm

Now,

$\sf{TSA\:of\:cylinder = 2\pi r(r+h)\:\:sq.units}$

= $\sf{TSA\:of\:cylinder = 2\times\dfrac{22}{7}\times21(21+6)}$

= $\sf{TSA\:of\:cylinder = 2\times3\times27}$

= $\sf{TSA\:of\:cylinder = 162\:\:cm^2}$

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11. Given:-

• Curved Surface Area of cylinder = 4400 cm²
• Circumference of its base = 110 cm

To find:-

Volume of the cylinder

Solution:-

We know,

Circumference of a circle = 2πr

Therefore,

$\sf{110 = 2\times\dfrac{22}{7}r}$

= $\sf{\dfrac{110\times7}{2\times22} = r}$

= $\sf{\dfrac{5\times7}{2} = r}$

= $\sf{\dfrac{35}{2} = r}$

= $\sf{r = 17.5\:cm}$

Now,

We know,

Curved Surface Area of cylinder = 2πrh sq.units

Therefore,

$\sf{4400 = 2\times\dfrac{22}{7}\times17.5\times h}$

= $\sf{\dfrac{4400\times7}{2\times22\times17.5} = h}$

= $\sf{\dfrac{200\times7\times10}{2\times175} = h}$

= $\sf{\dfrac{100\times10}{25} = h}$

= $\sf{h = 40\:cm}$

Now,

Volume of cylinder = πr²h cu.units

$\sf{Volume = \dfrac{22}{7}\times(17.5)^2\times40}$

= $\sf{Volume = \dfrac{22}{7}\times\dfrac{175}{10}\times{175}{10}\times40}$

= $\sf{Volume = 22\times35\times25}$

= $\sf{Volume = 19250\:cm^3}$

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Formulas:-

• Volume of cylinder = πr²h cu.units
• Curved Surface Area (CSA) of cylinder = 2πrh sq.units
• Total Surface Area (TSA) of cylinder = 2πr(r+h) sq.units.

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Answer 2

hii all answer are above