Question

The curved surface area of a right circular cylinder of height 14 cm is 88cm. Find the diameter of the base of the cylinder

Answer 1

Given :

• Curved Surface Area of Cylinder = 88cm²
• Height of Cylinder = 14cm

To Find :

• Diameter of base of Cylinder

Solution :

$\longrightarrow\tt{C.S.A\:of\:Cylinder=88{cm}^{2}}$

$\longrightarrow\tt{Height=14cm}$

Using Formula :

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

Putting Values :

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

$\longrightarrow\tt{88\times{7}=44\times{14}\times{r}}$

$\longrightarrow\tt{616=616r}$

$\longrightarrow\tt{r=\cancel\dfrac{616}{616}}$

$\longrightarrow\tt\bold{r=1cm}$

Now :

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

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

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

$\longrightarrow\tt\boxed{2cm}$

So, The Diameter of base of Cylinder is 2cm...

Answer 2

GIVEN :

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

TO FIND :

• Find the diameter of the base of the cylinder.

FIGURE :

$\setlength{\unitlength}{1 mm}\begin{picture}(5,5)\qbezier(2,3)(8,8)(14,3)\qbezier(2,3)(8,-4)(14,3)\put(2,-27){\line(0,2){30}}\put(14,-27){\line(0,2){30}}\qbezier(2,-27)(8,-35)(14,-27)\qbezier(2,-27)(8,-20)(14,-27)\put(8,-27){\line(0,2){30}}\put(15,-17){ \sf{h = 14cm} }\put(9,-29){ \tt{} }\put(8,-27){\line(2,0){6}}\put(8,3){\line(2,0){6}}\put(15,-14){ \tt{} }\end{picture}$

SOLUTION:

Let the radius of the base of the cylinder be r cm.

CSA of cylinder = 2πrh

88 = 2πrh

88 = 2 × 22/7 × r × 14

r = 88 × 7 / 2 × 22 × 14

r = 1

Therefore, radius of the base of the cylinder is 1 cm.

So,

Diameter = 2 × radius

Diameter = 2 × 1

Diameter = 2 cm

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