Question

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

Answer 1

Answer:

Given :-

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

To Find :-

• What is the diameter of the base of the cylinder.

Formula Used :-

$\clubsuit$ Curved Surface Area or CSA of Cylinder Formula :

$\mapsto \sf\boxed{\bold{\pink{C.S.A_{(Cylinder)} =\: 2{\pi}rh}}}$

where,

• C.S.A = Curved Surface Area
• π = pie or 22/7
• r = Radius
• h = Height

$\clubsuit$ Diameter Formula :

$\mapsto \sf\boxed{\bold{\pink{Diameter =\: 2r}}}$

where,

• r = Radius

Solution :-

First, we have to find the radius of cylinder :

Given :

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

According to the question by using the formula we get,

$\implies \bf 2{\pi}rh =\: 88$

$\implies \sf 2 \times \dfrac{22}{7} \times r \times 14 =\: 88$

$\implies \sf \dfrac{44}{7} \times 14r =\: 88$

$\implies \sf r =\: \dfrac{88 \times 7}{44 \times 14}$

$\implies \sf r =\: \dfrac{\cancel{616}}{\cancel{616}}$

$\implies \sf r =\: \dfrac{1}{1}$

$\implies \sf\bold{\purple{r =\: 1\: cm}}$

Hence, the radius of a cylinder is 1 cm .

Now, we have to find the diameter of a cylinder :

$\longrightarrow \bf Diameter =\: 2 \times Radius$

$\longrightarrow \sf Diameter =\: 2 \times 1$

$\longrightarrow \sf\bold{\red{Diameter =\: 2\: cm}}$

${\small{\bold{\underline{\therefore\: The\: diameter\: of\: the\: base\: of\: the\: cylinder\: is\: 2\: cm\: .}}}}$

Answer 2

Answer:

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

Step-by-step explanation:

Given :

➺ CSA of right circular cylinder = 88cm²

➺ Height of cylinder = 14cm

We know the formula :

➺ CSA of cylinder = 2πrh

Let's substitute the values and find the radius of the right circular cylinder :

➺ 2πrh = 88

➺ 2 × 22/7 × r × 14 = 88

➺ 2 × 22 × r × 2 = 88

➺ 4 × 22 × r = 88

➺ 88 × r = 88

➺ r = 88/88

➺ r = 1cm

∴ The radius of the right circular cylinder is 1cm.

Now, let's find the diameter of the base :

➺ Diameter = 2 × Radius

➺ D = 2 × 1cm

➺ D = 2cm

∴ The diameter of the base is 2cm.

Know more:

Some related formulae are :

➺ CSA of cube = 4a²

➺ TSA of cube = 6a²

➺ Volume of cube = a³

➺ CSA of cuboid = 2h (l + b)

➺ TSA of cylinder = 2 (lb + bh + hl)

➺ Volume of cuboid = lbh

➺ CSA of cone = πrl

➺ TSA of cone = πr (r + l)

➺ Volume of cone = ⅓ πr²h