Question

the curved surface area of a right circular cylinder is 440cm2 and its radius is 7cm its height​

Answer 1

Answer:

10 cm

Step-by-step explanation:

As per the provided information in the given question, we have :

• C.S.A of the right circular cylinder = 440 cm²
• Base radius = 7 cm

We are asked to calculate its height. Let us assume the height as h.

― In order to calculate the height, we'll be using the formula of C.S.A of the right circular cylinder which shall act as a linear equation here. As it is known to us that,

$\longrightarrow \sf{\quad { C.S.A_{(Cylinder)} = 2\pi rh }}$

Substitute the values we have.

$\longrightarrow \sf{\quad { 440 = 2 \times\dfrac{22}{7} \times 7 \times h }}$

Dividing 7 by 7.

$\longrightarrow \sf{\quad { 440 = 2 \times 22 \times h }}$

Performing multiplication in RHS.

$\longrightarrow \sf{\quad { 440 = 44 \times h }}$

Transposing 44 from RHS to LHS. Its arithmetic operator will get changed.

$\longrightarrow \sf{\quad {\cancel{\dfrac{ 440 }{44}}= h }}$

Dividing 440 by 44.

$\longrightarrow \quad \underline{\boxed { \textbf{\textsf{10 \; cm = h}} }}$

Therefore, height of the cylinder is 10 cm.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Learn More :

$\large {\underline { \sf {Right \; Circular \; Cylinder :}}}$

• Volume = πr²h
• Curved surface area = 2πrh
• Total surface area = 2πr(r + h)

$\large {\underline { \sf {Hollow \; Cylinder :}}}$

• Volume = π (R² – r²) h
• Curved surface area = 2π(R + r)h
• Total surface area = 2π(R + r)(h + R – r)

_

• r = inner radius
• R = outer radius

Answer 2

$\frak{Given\:\:}\begin{cases}\sf \:\:The\:\: \:Curved \:Surface \:Area\:of \:Cylinder \:is\:\frak{440\: cm^2\:}\:\\\\ \sf \:\: The\:\: \:Radius\:of \:Cylinder \:is\:\frak{7\:cm\:}\:\end{cases}$

Exigency To Find : The Height of Cylinder ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Height of Cylinder be h cm .

⠀⠀▪︎ We've Radius and Curved surface area of Cylinder , we will find Height of Cylinder using the Formula to find Curved Surface Area of Cylinder .

》 Formula to find Curved Surface Area of Cylinder is Given by —

$\\\qquad \star\:\:\underline {\boxed {\pmb {\frak{ \:\:C.S.A \:_{(\:Cylinder \:)}\:\:=\:\: 2 \pi \:r\:h \:sq.units \:}}}}$

⠀⠀⠀⠀⠀Here , r is the Radius of Cylinder &h is the Height of the Cylinder .

$\underline {\dag\frak{\:Putting \:known \:Values \:in \:Formula \:\::\:}}$

$\qquad :\implies \sf \:\:C.S.A \:_{(\:Cylinder \:)}\:\:=\:\: 2 \pi \:r\:h \:\\\\\\ \qquad :\implies \sf \:\:440\:\:\:=\:\: 2 \times \:\dfrac{22}{7} \:\times \:7 \:\times \:h \:\\\\\\ \qquad :\implies \sf \:\:\cancel {\dfrac{440}{2}}\:\:\:=\:\: \:\dfrac{22}{7} \:\times \:7 \:\times \:h \:\\\\\\ \qquad :\implies \sf \:\:220\:\:\:=\:\: \:\dfrac{22}{\cancel {7}} \:\times \:\cancel {7} \:\times \:h \:\\\\\\ \qquad :\implies \sf \:\:220\:\:\:=\:\: \:22 \: \:\times \:h \:\\\\\\ \qquad :\implies \sf \:\: h\:\:\:=\:\: \:\cancel {\dfrac{220}{22}} \: \:\:\\\\\\ \qquad :\implies\underline {\boxed{\pmb{\frak{\purple { \:\: h\:\:\:=\:\: \:10\:cm\:}}}}}\:\:\bigstar \:\: \:\:$

$\therefore \:\underline {\sf Hence, \:Height \:of \:Cylinder \:is \:\pmb{\bf 10 \:cm \:}\:.\:}$