Answer:
Radius = 21 cm
Volume = 34636.1 cm³
Step-by-step explanation:
The circumference of the base of a cylinder with radius r is given by the formula:
[tex]C = 2 \pi r[/tex]
Given the circumference is 132 cm, we substitute to get
[tex]2 \pi r = 132\\\\r = \dfrac{132}{2\pi}\\\\\r = 21 \text{cm to the nearest cm}[/tex]
The volume of a right cylinder of radius r and height h is given by the formula
[tex]V = \pi r^2 h[/tex]
Plugging in r = 21 and h = 25 we get
[tex]V = \pi \cdot 21^2\cdot25[/tex]
[tex]V = 34636.1 \;cm^3[/tex]
The radius of the cylindrical vessel with a circumference of 132 cm is 21 cm, and the volume of the cylinder, given a height of 25 cm, is 34575 cm³.
The student asked to find the radius and the volume of a cylindrical vessel with a given circumference of the base and height. The first step is to find the radius of the cylinder. The circumference (C) of a circle is given by the formula C = 2πr, where r is the radius. Given that the circumference is 132 cm, we can solve for the radius (r) as follows:
r = C / (2π) = 132 cm / (2×3.14) = 21 cm.
Therefore, the radius of the cylindrical vessel is 21 cm.
Next, we calculate the volume of the cylinder (V) using the formula V = πr²h, where r is the radius and h is the height. Substituting the calculated radius and given height (25 cm) into the formula:
V = π(21 cm)²×25 cm = 3.14 × 441 cm² × 25 cm = 34575 cm³.
The volume of the cylinder is 34575 cm³.
