Question

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2

. Find the diameter of the base of the cylinder.​

Answer 1

$\frak{Given}\begin{cases}&\sf{Height\; of\; cylinder = \frak{14\;cm}}\\ \ &\sf{CSA\; of\; cylinder=\frak{88\:cm^2}}\end{cases}$

Need to find: The diameter of the base of the cylinder.

❍ Let the radius of the right circular cylinder be r cm respectively.

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Curved\; Surface\;Area\: :}}$⠀⠀⠀⠀

To calculate CSA (Curved Surface Area) of the cylinder formula is Given by :

$\bf{\dag}\;\;\underline{\boxed{\sf{CSA_{\;(cylinder)} = 2\pi r h}}}$

where,

• r is radius
• h is height (14 cm)
• CSA is 88 cm²

$\rule{100px}{.3ex}$

$:\implies\sf 2 \pi r h = 88\\\\\\:\implies\sf 2\times \dfrac{22}{7}\times r \times (14) = 88 \\\\\\:\implies\sf r = \cancel\dfrac{88 \times 7}{2 \times 22 \times 14}\\\\\\:\implies{\underline{\boxed{\frak{\pink{r = 1\; cm}}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence, \; radius\;of\; the\: cylinder\;is\:\textbf{1 cm}.}}}$

$\rule{250px}{.3ex}$

$\bigstar\;\boxed{\sf{Diameter = 2 \times Radius}}$

↠ Diameter = 2 × Radius

↠ Diameter = 2 × 1

↠ Diameter = 2 cm

$\therefore{\underline{\textsf{Hence, \; Diameter\; of\;the\;base\;of\: cylinder\;is\:\textbf{2 cm}.}}}$

Answer 2

Answer:

Given :-

CSA of cylinder = 88 cm²

Height of cylinder = 14 cm

To Find :-

Diameter

Concept :-

In order to solve we need to first find the radius of the cylinder. We may find the radius by assuming the radius as r and by putting the value in CSA. We need to find Diameter by multiplying radius by 2

We need to use some formula

CSA = 2πrh

Diameter = 2 × Radius

Solution :-

Let the radius be r

${ \boxed { \implies { \sf \: 88 = 2 \times \dfrac{22}{7} \times r \times 14}}}$

${ \boxed{ \implies{ \sf \: 88 = 2 \times 22 \times r \times 2}}}$

${ \boxed{ \implies { \sf \: 88 = 88r}}}$

${ \boxed{ \implies{ \sf \: r = \dfrac{88}{88} }}}$

${ \textsf{ \textbf{ \underline{Radius \: = 1 \: cm}}}}$

Finding Diameter

${ \boxed{ \implies{ \sf \: Diameter = 2 \times r}}}$

${ \boxed { \implies{ \sf \: Diameter = 2 \times 1}}}$

${ \textsf{ \textbf{ \pink{ \underline{Diameter = 2 \: cm}}}}}$

Hence,

• Diameter of base is 2 cm