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
[tex]\begin{gathered}\end{gathered}[/tex]
TO FIND :
in the provided question we need to find :
- ➠ Radius of cylinder
- ➠ Diameter of cylinder
[tex]\begin{gathered}\end{gathered}[/tex]
USING FORMULAS :
[tex]\star{\underline{\boxed{\sf{\purple{Csa = 2 \pi rh}}}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\purple{d = 2r}}}}}[/tex]
- ➛ Csa = Curved surface area
- ➛ π = 22/7
- ➛ r = radius
- ➛ h = height
- ➛ d = diameter
[tex]\begin{gathered}\end{gathered}[/tex]
SOLUTION :
Firstly, finding the radius of cylinder by substituting the values in the formula :
[tex] \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}[/tex]
Hence, the radius of cylinder is 1 cm.
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Now, finding the diameter of cylinder by substituting the values in the formula :
[tex]\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}[/tex]
Hence, the diameter of the base of the cylinder is 2 cm.
[tex]\rule{300}{2.5}[/tex]
