Question

Circular cylinder,14cm long is 88cm square .if the volume of the metal used in making the cylinder is 176cm cube .find outer and inner diameter of the cylinder

Answer 1

Given that,

Length = 14 cm

Area of cylinder = 88 cm²

Volume of the cylinder = 176 cm³

Let the outer radius is R and inner radius is r.

We need to calculate the outer radius

Using curved surface area of hollow cylinder

$A=2\pi(R-r)h$

Put the value into the formula

$88=2\pi(R-r)14$

$R-r=\dfrac{88}{2\pi\times14}$

$R-r=1$....(I)

Using formula of volume of hollow cylinder

$V=\pi(R^2-r^2)h$

$176=\pi(R^2-r^2)14$

$R^2-r^2=\dfrac{176}{\pi\times14}$

$R^2-r^2=4$

$(R-r)(R+r)=4$

Put the value into the formula

$R+r=4$.....(II)

From equation (I) and (II)

$2R=5$

$R=\dfrac{5}{2}$

$R=2.5\ cm$

The outer diameter of the cylinder is 5.0 cm.

We need to calculate the inner radius

Put the value of R in the equation (I)

$2.5-r=1$

$-r=1-2.5$

$r=1.5\ cm$

The inner diameter of the cylinder is 3.0 cm.

Hence, The outer diameter of the cylinder is 5.0 cm.

The inner diameter of the cylinder is 3.0 cm.