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

____

$2 \times \frac{22}{7} \times r \times 14 = 88 cm²$

$2 \times \frac{22}{1} \times r \times2 \: = 88 cm²$

$2 \times 22 \times r \times 2 = 88 cm²$

$88r = 88 cm²$

$r = \frac{88}{88}$

$r = 1$

____

Diameter = radius + radius

= 1 + 1

= 2

____

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

Answer 2

Answer:

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

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 :

$\begin{gathered} \qquad{\longrightarrow{\sf{Csa = 2 \pi rh}}} \\ \\ \qquad{\longrightarrow{\sf{88 = 2 \times \dfrac{22}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{7} \times r \times 14}}} \\ \\ \qquad{\longrightarrow{\sf{88 =\dfrac{44}{\cancel{7}}\times r \times \cancel{ 14}}}} \\ \\ \qquad{\longrightarrow{\sf{88 =44 \times r \times 2}}} \\ \\ \qquad{\longrightarrow{\sf{88 =88 \times r}}} \\ \\ \qquad{\longrightarrow{\sf{r = \frac{88}{88}}}} \\ \\ \qquad{\longrightarrow{\underline{\underline{\sf{\pink{r = 1 \: cm}}}}}} \end{gathered}$

Hence, the radius of cylinder is 1 cm.

———————————————————————

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

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

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

$\rule{300}{2.5}$