Question

the curvedsurface area of a right circular cylinder of height 14cm is 176cm².the diameter of the base is ​

Answer 1

Given :

• The curved surface area of a right circular cylinder is 176 cm².
• Height of the cylinder = 14 cm

To find :

• Diameter of the base.

Solution :

Consider,

• Radius of the cylinder = r cm
• Diameter of the cylinder = 2r cm

Height of cylinder ( h) = 14 cm

Formula Used :-

★ ${\boxed{\bold{CSA\:of\: cylinder=2\pi\:rh}}}$

$\to\sf{CSA=2\times\dfrac{22}{7}\times\:r\times\:14\:cm^2}$

$\to\sf{CSA=88r\:cm^2}$

${\underline{\sf{According\:to\: the\: question:-}}}$

$\mapsto\sf{88r=176}$

$\mapsto\sf{r=\dfrac{176}{88}}$

$\mapsto\sf{r=2}$

• Radius = 2 cm

Diameter of the base = 2r

→ Diameter of the base = ( 2 × 2 ) cm

→ Diameter of the base = 4 cm

Therefore, diameter of the base is 4 cm.

Answer 2

☣ Qᴜᴇsᴛɪᴏɴ ☣

➥ The curvedsurface area of a right circular cylinder of height 14 cm is 176 cm².the diameter of the base is

⛦ Aɴsᴡᴇʀ ⛦

➥ Diameter of the base = 4 cm

☄ Gɪᴠᴇɴ ☄

➥ C.S.A = 176 cm²

➥ Height = 14 cm

⚛ Tᴏ Fɪɴᴅ ⚛

➥ Diameter of the base = ?

⠀⠀⠀

❏ According To Given Question

⠀⠀⠀

↗ Let r be the radius and h be the height of cylinder

❈ As we know that the formula for finding the value of C.S.A is ፦

$\displaystyle{:\implies\bf{2\pi rh}}$

⤵ On putting the value of formula, we get

$\displaystyle {\sf{: \implies 2 \times \frac{22}{ \cancel{ \: 7 \: }} \times \cancel{14} = 176}} \\ \\ \sf{: \implies 2 \times 22 \times 2 = 176}\\ \\ \sf{: \implies 88r = 176 } \\ \\ \sf{: \implies r = \frac{ \cancel{176}}{ \cancel{88}} } \\ \\ \sf{: \implies \bf{ \underline{ \boxed{ \green{ \bf{ \: \: r = 2 \: cm \: \: }}}}}}\\ \\ \rm{ \underline{Now,}}$

❈ As we know that the formula for finding the value of diameter is ፦

$\sf{ : \implies\bf{ Diameter = 2r}}$

⤵ On putting the value of formula, we get

$\sf{ : \implies Diameter\: of \:the \:base= 2 \times 2} \\ \\ \sf{ : \implies Diameter \: of \: the \: base = \underline{\boxed{ \bf{ \purple{ \: \: 4 \: cm \: \: }}}}}$