Question

11 i) Find the volume of a right circular cylinder whose curved surface area and
height are 110 cm³ and 5 cm respectively. Ans: 192.5 cm?​

Answer 1

✬ The volume of right circular cylinder is 192.5 cm³ ✬

Step-by-step explanation:

Given: The curved surface area of cylinder is 110 cm³ and the height of cylinder is 5 cm respectively.

To find: Volume of right circular cylinder

Required formula:

• Volume of right circular cylinder = πr²h
• Curved surface area of cylinder = 2πrh

Here,

• CSA = curved surface area of cylinder
• V = Volume of right circular cylinder
• h = height
• r = radius

Finding the radius of cylinder,

$\\ \implies \sf{CSA = 2\pi rh} \\ \\ \implies \sf{110 =2 \times \frac{22}{7} \times r \times 5} \\ \\ \implies \sf{110 = \frac{44}{7} \times r \times 5} \\ \\ \implies \sf{ 110 = \frac{220}{7} \times r} \\ \\ \implies \sf{110 \times 7 = 220 \times r} \\ \\ \implies \sf{770 = 220r} \\ \\ \implies \sf{r = \cancel{\frac{770}{220}} } \\ \\ \: \: \: \: \: \: \: \: \bullet \: \: \underline{ \boxed{\frak{r = 3.5}}} \: \red{ \bigstar}$

• Therefore,the radius of cylinder is 3.5 cm.

Now,finding the volume of right circular cylinder,

$\\ \implies\sf{V = \pi r^2 h}\\ \\ \implies\sf{V = \frac{22}{7}\times (3.5)^2 \times 5}\\ \\ \implies\sf{V = \frac{22}{ \cancel{7}}\times \cancel{3.5} \times 3.5 \times 5} \\ \\ \implies\sf{V = 22 \times 0.5 \times 3.5 \times 5} \\ \\ \implies\sf{V = 11 \times 17.5} \\ \\ \: \: \: \: \: \: \bullet \: \: \: \underline{\boxed{\frak{V = 192.5 \: {cm}^{3}}}} \: \blue{ \bigstar}$

• Hence,The volume of right circular cylinder is 192.5 cm³ .