The problem describes a cylinder with diameter $d = 10$ cm and length (height) $h = 38$ cm. We need to find: (a) The circumference of the base. (b) The volume of the cylinder. (c) The area of the base. We are then asked to find the total surface area of a similar cylinder.

1. Problem Description

The problem describes a cylinder with diameter $d = 10$ cm and length (height) $h = 38$ cm. We need to find:

(a) The circumference of the base.

(b) The volume of the cylinder.

(c) The area of the base.

We are then asked to find the total surface area of a similar cylinder.

2. Solution Steps

(a) The circumference of the base is given by the formula:

$C = \pi d$

$C = \pi (10)$

$C = 10\pi$ cm

Assuming we want an approximate answer, use $\pi \approx 3.14159$:

$C \approx 10 \times 3.14159 = 31.4159$ cm

(b) The volume of the cylinder is given by the formula:

$V = \pi r^2 h$

Where $r$ is the radius and $h$ is the height. Since $d = 10$, $r = d/2 = 10/2 = 5$ cm.

$V = \pi (5^2) (38)$

$V = \pi (25) (38)$

$V = 950\pi$ cm$^3$

Assuming we want an approximate answer, use $\pi \approx 3.14159$:

$V \approx 950 \times 3.14159 = 2984.5105$ cm$^3$

(c) The area of the base is given by the formula:

$A = \pi r^2$

$A = \pi (5^2)$

$A = 25\pi$ cm$^2$

Assuming we want an approximate answer, use $\pi \approx 3.14159$:

$A \approx 25 \times 3.14159 = 78.53975$ cm$^2$

The problem then asks us to calculate the total surface area of the similar cylinder. The total surface area of a cylinder is:

$SA = 2\pi r h + 2\pi r^2 = 2\pi r (h + r)$

For this cylinder:

$SA = 2\pi (5) (38+5) = 10\pi (43) = 430\pi$ cm$^2$

Assuming we want an approximate answer, use $\pi \approx 3.14159$:

$SA \approx 430 \times 3.14159 = 1350.8837$ cm$^2$

3. Final Answer

(a) The circumference of the base is $10\pi$ cm (approximately $31.42$ cm).

(b) The volume of the cylinder is $950\pi$ cm$^3$ (approximately $2984.51$ cm$^3$).

(c) The area of the base is $25\pi$ cm$^2$ (approximately $78.54$ cm$^2$).

The total surface area is $430\pi$ cm$^2$ (approximately $1350.88$ cm$^2$).