The problem describes a cylinder with a diameter of $14 cm$ and a length of $25 cm$. We need to find: (i) the circumference of the base, (ii) the volume of the cylinder, and (iii) the area of the base.

1. Problem Description

The problem describes a cylinder with a diameter of $14 cm$ and a length of $25 cm$. We need to find:

(i) the circumference of the base,

(ii) the volume of the cylinder, and

(iii) the area of the base.

2. Solution Steps

(i) Circumference of the base:

The circumference of a circle is given by $C = \pi d$, where $d$ is the diameter.

Given the diameter $d = 14 cm$, we have

$C = \pi (14) = 14\pi cm$.

Using $\pi \approx 3.142$, we get

$C \approx 14 \times 3.142 = 43.988 cm$.

(ii) Volume of the cylinder:

The volume of a cylinder is given by $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height (length).

Since the diameter is $14 cm$, the radius is $r = \frac{14}{2} = 7 cm$.

The height (length) of the cylinder is $h = 25 cm$.

$V = \pi (7^2) (25) = \pi (49)(25) = 1225 \pi cm^3$.

Using $\pi \approx 3.142$, we get

$V \approx 1225 \times 3.142 = 3848.95 cm^3$.

(iii) Area of the base:

The area of the base (circle) is given by $A = \pi r^2$.

$r = 7 cm$, so

$A = \pi (7^2) = 49\pi cm^2$.

Using $\pi \approx 3.142$, we get

$A \approx 49 \times 3.142 = 153.958 cm^2$.

3. Final Answer

(i) Circumference of the base: $14\pi cm \approx 43.988 cm$

(ii) Volume of the cylinder: $1225\pi cm^3 \approx 3848.95 cm^3$

(iii) Area of the base: $49\pi cm^2 \approx 153.958 cm^2$