Question

If the sum of radius and height of cylinder is 21cm and curved surface area 616 cm2, find the total surface area of cylinder.

please help me to find the solution..​

Answer 1

Given:-

• Sum of radius and height = 21cm
• Total surface area = 616cm²

Find:-

• Curved surface area of cylinder.

Solution:-

we, know that

$\huge{\boxed{\underline{\sf Total\:Surface\: Area \:of \:Cylinder=2\pi r(r+h)}}}$

$\sf where\small{\begin{cases}\sf r+h = 21cm\\\sf Total\: surface\:area=616cm^2\end{cases}}$

$\pink\bigstar$ Substituting these values:-

➨$\sf Total\:Surface\: Area=2\pi r(r+h)$

➨$\sf 616=2\times \dfrac{22}{7} r(r+h)$

➨$\sf 616=\dfrac{44}{7} r(21)$

➨$\sf 616\times\dfrac{7}{44}=21r$

➨$\sf \dfrac{4312}{44}=21r$

➨$\sf 98=21r$

➨$\sf \dfrac{98}{21}=r$

➨$\sf 4.66cm(approx.)=r$

➨$\sf r=4.6cm$

_____________________________

→r + h= 21cm

→4.6 + h = 21

→h = 21-4.6

→h = 16.4cm

Now, using

$\huge{\boxed{\underline{\sf Curved\:Surface\: Area \:of \:Cylinder=2\pi rh}}}$

$\sf where\small{\begin{cases}\sf r= 4.6cm\\\sf h=16.4cm\end{cases}}$

$\red\bigstar$ Substituting these values:-

➲$\sf Curved\:Surface\: Area=2\pi rh$

➲$\sf Curved\:Surface\: Area=2\times \dfrac{22}{7}\times 4.6\times 16.4$

➲$\sf Curved\:Surface\: Area= \dfrac{44}{7}\times 75.44$

➲$\sf Curved\:Surface\: Area= \dfrac{3319.36}{7}$

➲$\sf Curved\:Surface\: Area= 474.19cm^2(approx.)$

➲$\sf Curved\:Surface\: Area= 474.2cm^2(approx.)$

[tex]\underline{\boxed{\sf\therefore Curved\: surface\: area\:is\:474.2cm^2}}

Answer 2

$\huge\underline{\bf \orange{Answer :}}$

we, know that

TotalSurfaceAreaofCylinder=2πr(r+h)

where{ r+h=21cm, Total surface area =616cm²

Substituting these values:-

➨Total Surface Area=2πr(r+h)

➨616=2× 7/22 r(r+h)

➨616= 744 r(21)

➨616× 447 =21r

➨44/4312 =21r

➨98 = 21r

➨21/98 = r

➨4.66cm(approx.) = r

➨r=4.6cm

_____________________________

> r + h= 21cm

> 4.6 + h = 21

> h = 21-4.6

> h = 16.4cm

Now, using

Curved Surface Area of Cylinder=2πrh

where{ r=4.6cm, h=16.4cm}

Substituting these values:-

=> Curved Surface area=2πrh

=> Curved surface area=2× 22⁷ ×4.6×16.4

=> Curved surface area= 44/7 ×75.44

=> Curved surface area=474.19cm² (approx.)

=> Curved surface area=474.2cm² (approx.)