Question

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

Answer 1

CSA of a cylinder = 88 cm²

height = 14 cm

diameter = ?

CSA of a cylinder = 88 cm²

2πrh = 88 cm²

____

`2 * (22)/(7) * r * 14 = 88 cm²`

`2 * (22)/(1) * r *2 \: = 88 cm²`

`2 * 22 * r * 2 = 88 cm²`

`88r = 88 cm²`

`r = (88)/(88)`

`r = 1`

____

Diameter = radius + radius

= 1 + 1

= 2

____

Therefore, The Diameter of the base of the cylinder is 2.

Answer 2

The diameter of the base of the cylinder is 2 cm.

Step-by-step Step-by-step explanation:

GIVEN :

As per given question we have provided that :

• ➣ Height of cylinder = 14 cm
• ➣ Curved surface area = 88 cm²

`\begin{gathered}\end{gathered}`

TO FIND :

in the provided question we need to find :

• ➠ Radius of cylinder
• ➠ Diameter of cylinder

`\begin{gathered}\end{gathered}`

USING FORMULAS :

`\star{\underline{\boxed{\sf{\purple{Csa = 2 \pi rh}}}}}`

`\star{\underline{\boxed{\sf{\purple{d = 2r}}}}}`

• ➛ Csa = Curved surface area
• ➛ π = 22/7
• ➛ r = radius
• ➛ h = height
• ➛ d = diameter

`\begin{gathered}\end{gathered}`

SOLUTION :

Firstly, finding the radius of cylinder by substituting the values in the formula :

`\begin{gathered} \qquad{\longrightarrow{\sf{Csa = 2 \pi rh}}} \\ \\ \qquad{\longrightarrow{\sf{88 = 2 * (22)/(7) * r * 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =(44)/(7) * r * 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\frac{44}{\cancel{7}}* r * \cancel{ 14}}}} \\ \\ \qquad{\longrightarrow{\sf{88 =44 * r * 2}}} \\ \\ \qquad{\longrightarrow{\sf{88 =88 * r}}} \\ \\ \qquad{\longrightarrow{\sf{r = (88)/(88)}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\pink{r = 1 \: cm}}}}}} \end{gathered}`

Hence, the radius of cylinder is 1 cm.

———————————————————————

Now, finding the diameter of cylinder by substituting the values in the formula :

`\begin{gathered} \qquad{\longrightarrow{\sf{d = 2r}}} \\ \\ \qquad{\longrightarrow{\sf{d = 2 * 1}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\red{r = 2 \: cm}}}}}}\end{gathered}`

Hence, the diameter of the base of the cylinder is 2 cm.

`\rule{300}{2.5}`