Question

the curved surface area of a right circular cylinder of height 14cm is 88cm sq the diameter of the base is:​

Answer 1

Given :

• Height of Cylinder is 14 cm .
• Curved Surface Area of Cylinder is 88 cm² .

To Find :

• Diameter of the base of Cylinder .

Solution :

$\longmapsto\tt{Height=14\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{88=2\times\dfrac{22}{{\cancel{7}}}\times{r}\times{{\cancel{14}}}}$

$\longmapsto\tt{88=2\times{22}\times{r}\times{2}}$

$\longmapsto\tt{88=88\:r}$

$\longmapsto\tt{r=\cancel\dfrac{88}{88}}$

$\longmapsto\tt\bf{r=1\:cm}$

Radius of Cylinder is 1 cm ..

Now ,

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{Diameter=2r}$

$\longmapsto\tt{2(1)}$

$\longmapsto\tt\bf{2\:cm}$

So , The Diameter of Radius is 2 cm ..

_______________________

• C.S.A of Cylinder = 2πrh
• T.S.A of Cylinder = 2πr(r+h)
• Volume of Cylinder = πr²h

Here :

• r = radius of Cylinder
• h = height of Cylinder
• π = 22/7 or 3.14

_______________________

Answer 2

Answer:

Given :-

• The curved surface area of a right circular cylinder of height is 14 cm is 88 cm sq.

To Find :-

• What is the diameter of a base .

Formula Used :-

First, we have to find the Curved surface area,

$\boxed{\bold{\small{C.S.A\: =\: 2{\pi}rh}}}$

Now, we have to find the diameter,

$\boxed{\bold{\small{Diameter\: =\: 2\: ×\: radius}}}$

Solution :-

Let, the radius be r

Given :

• h = 14 cm
• C.S.A = 88 cm sq

According to the question by using the formula we get,

❑ Curved surface area = 2πrh

↦ 2πrh = 88

↦ 2 × $\dfrac{22}{7}$ × r × 14 = 88

↦ r = $\dfrac{88 × 7}{2 × 22 × 14}$

↦ r = $\sf\dfrac{\cancel{616}}{\cancel{616}}$

➠ r = 1 cm

Hence, the radius is 1 cm

Now, we have to find the diameter,

❐ Diameter = 2 × radius

↦ Diameter = 2 × 1

$\longrightarrow$ Diameter = 2 cm

$\therefore$ The diameter of a base is 2 cm .