Question

The curved surface area of a cylinder is 6160 cm2 and the circumference of the base is
176 cm. Find the volume of the cylinder​

Answer 1

Answer:

86,240cm³

Step-by-step explanation:

Given in the picture....

I hope it will help you...

Answer 2

${ \large { \underline{ \pmb{ \sf{Given.... }}}}}$

★ The curved surface area of a cylinder is 6160 cm²

★ the circumference of the base is 176 cm.

${ \large { \underline{ \pmb{ \sf{To \: Find .... }}}}}$

★ Find the volume of the cylinder

${ \large { \underline{ \pmb{ \sf{Solution .... }}}}}$

★ The volume of the cylinder is 86,240cm³

${ \large { \underline{ \pmb{ \sf{Full \: Solution .... }}}}}$

~ Now let's find the radius of the cylinder whith the helps of the circumference given [ 176cm]

✪ Formula to find the circumference of the base

➼ Circumference of a circle = 2πr

~ Now let's use this formula to find the radius of the cylinder

${ : \implies} \sf \: Circumference \: of \: the \: circle = 2\pi \: r$

${ : \implies} \sf \: 176cm = 2 \times \dfrac{22}{7} \times r$

${ : \implies} \sf \: \: r = \dfrac{176 \times 7}{22 \times 2}$

${ : \implies} \sf \: r = \dfrac{1232}{44}$

${ : \implies} \sf \:{ \boxed{ \pmb{ \frak{ R= 28cm}}}}$

• Henceforth the radius of the cylinder is 28cm

~As we have found the radius let's find the hieght of the cylinder with the help of its curved surface area given [6160cm²]

✪ Formula to find the curved surface area

➼Curved Surface area of a cylinder = 2πrh

~ Now let's find the hieght of the cylinder using this formula

${ : \implies} \sf \: curved \: surface \: area = 2\pi \: rh$

${ : \implies} \sf \: 6160 {cm}^{2} = 2 \times \dfrac{22}{7} \times 28 \times h$

${ : \implies} \sf \: h = \dfrac{6160 \times 7}{2 \times 22 \times 28}$

${ : \implies} \sf \: h = \dfrac{43120 {cm}^{2} }{1232cm}$

${ : \implies} \sf \:{ \boxed{ \pmb{ \frak{h = 35cm}}}}$

• Henceforth the hieght of the cylinder is 35cm

~ Now let's find the volume of the cylinder

✪ Formula to find the volume of the cylinder

➼ Volume of a cylinder is πr²h

~ Now let's substitute the values

${ : \implies} \sf \: volume \: = \pi {r}^{2} h$

${ : \implies} \sf \: volume = \dfrac{22}{7} \times {28}^{2} \times 25$

${ : \implies} \sf \: volume = 22 \times 28 \times 28 \times 5$

${ : \implies} \sf \: volume = { \boxed{ \pmb{ \frak{8624 {cm}^{3} }}} \bigstar}$

• Henceforth the volume of the cylinder is 86250cm³