Question

Curved surface area and circumference at the base of a solid right circular cylinder are 4400 sq. cm and 110 cm respectively. Find its height and diameter.

Answer 1

Hint: The curved surface area of the right circular cylinder is given by \[2\pi rh\] and circumference at the base of the right circular cylinder is given by \[2\pi r\]. As we know the value of these two by substituting \[2\pi r\] value in curved surface area we will get the height of the cylinder. Then we will calculate the radius of the base and then we will get diameter.

Complete step-by-step solution -

Given, Curved surface area of solid right circular cylinder =4400 sq. cm.
Circumference at the base of solid right circular cylinder =110cm
We know that the formula for curved surface area of cylinder is given by \[2\pi rh\]
\[2\pi rh = 4400sq.cm\]
\[2\pi r\] = 110(because it is the circumference at the base of right circular cylinder and it is given as 110cm)
\[(110)h=4400\]. . . . . . . . . . . . . . .(1)
\[h=\dfrac{4400}{110}\]. . . . . . . . . . . . . (2)
\[h=40cm\]
So, the height of cylinder we obtained is 40cm
We know that the formula for circumference at the base of right circular cylinder is given by \[2\pi r\]
\[\Rightarrow 2\pi r = 110cm\]. . . . . . . . . . . (3)
\[\Rightarrow 2\times \dfrac{22}{7}\times r = 110\]. . . . . . . . . .(4)
\[\Rightarrow r = \dfrac{35}{2}\]
\[\Rightarrow r = 17.5cm\]
The diameter is given by 2r so, diameter= \[2r = 2\left( \dfrac{35}{2} \right) = 35cm\]
Hence the diameter of the cylinder we obtained is 35cm.

Note: The base of the right circular cylinder is a circle and its circumference is given by \[2\pi r\]. Note that the curved surface area of the cylinder and total surface area of the cylinder are different. The formula for the curved surface area of the cylinder is given by \[2\pi rh\] and the total surface area is given by \[2\pi r(r+h)\].