Question

The volume and CSA of a cylinder is 2310 cm and 660 cm respectively find its base radius and height​

Answer 1

$\large\underline\pink{Given:-}$

• The volume and CSA of a cylinder is 2310 cm and 660 cm.

$\large\underline\pink{To find:-}$

• Fine the the base radius and height ....?

$\large\underline\pink{Solutions:-}$

• Volume of cylinder = 2310cm²
• CSA of cylinder = 660cm²

CSA of cylinder = 2πrh

660 = 2 × 22/7 × rh

660 × 7 / 44 = rh

105 = rh

Volume of cylinder = πr²h

2310 = 22/7 × r × rh

2310 = 22/7 × r × 105

2310 × 7 / 22 × 105 = r

210 / 2 × 105 = r

14 / 2 = r

7 = r

r = 7cm

Now, putting the value of r in eq (i).

105 = rh

105 = 7 × h

105/7 = h

15 = h

h = 15cm

Hence, the base of radius is 7cm and height is 15cm.

Answer 2

Given:-

• Volume of cylinder= 2310cm
• CSA of cylinder = 660cm

To find:-

• The base radius and height of cylinder.

Solution:-

$\sf \: CSA \: of \: cylinder = 660cm \\ \\ \sf \: 2\pi \: rh = 660 \\ \\ \sf \: 2 \times \frac{22}{7} \times rh = 660m \\ \\ \sf \: r \times h = \frac{660 \times 7}{44} \\ \\ \sf \: r \times h = 105.....eq.1$

Now,

$\sf \implies \: Volume \: of \: cylinder = \pi \: r {}^{2} h \\ \\ \sf\implies \: 2310 = \dfrac{22}{7} \times r \times r \times h \\ \\ \sf\implies \: 2310 = \dfrac{22}{7} \times 105 \times r... (\because \: from \: eq.1) \\ \\ \sf\implies \: r = \dfrac{2310 \times 7}{22 \times 105} \\ \\ \sf\implies \: r = \dfrac{735}{105} \\ \\ \sf \: \implies \boxed{\boxed{ \purple{ \bf{r = 7cm}}}}$

Put r = 7cm in equation 1,

$\sf \: \implies \: r \times h = 105 \\ \sf \implies 7 \times h = 105 \\ \sf \implies \: h = \frac{105}{7} \\ \sf \implies \: \boxed{ \boxed{ \purple{\bf{h = 15cm}}}}$