The volume of the right cylinder is [tex]\boxed{36\pi {\text{ unit}}{{\text{s}}^3}}.[/tex]
Further explanation:
The formula for the volume of the cylinder can be expressed as,
[tex]\boxed{{\text{Volume}} = \pi {r^2}h}[/tex]
Here, ‘r” represents the radius of the cylinder and “h” represents the height of the cylinder.
Given:
The radius of the cylinder is [tex]{\text{3 units}}[/tex] and the height of the cylinder is [tex]{\text{4 units}}[/tex] and the slant height is [tex]5{\text{ units}}[/tex]
The options of the volume are given as follows.
A. [tex]{\text{72}}\pi {\text{uni}}{{\text{t}}^3}[/tex]
B. [tex]36\pi {\text{uni}}{{\text{t}}^3}[/tex]
C. [tex]45\pi {\text{uni}}{{\text{t}}^3}[/tex]
D. [tex]90\pi {\text{uni}}{{\text{t}}^3}[/tex]
Explanation:
The volume of the right cylinder can be obtained as follows,
[tex]\begin{aligned}{\text{Volume}} &= \pi {r^2}h\\&= \pi\times {\left( 3 \right)^2} \times 4\\&= \pi \times 9 \times 4\\&= 36\pi\\\end{aligned}[/tex]
The volume of the cylinder is [tex]36\pi {\text{ unit}}{{\text{s}}^3}.[/tex]
Option A is not correct.
Option B is correct.
Option C is not correct.
Option D is not correct.
Hence, the volume of the right cylinder is [tex]\boxed{36\pi {\text{ unit}}{{\text{s}}^3}}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Mensuration
Keywords: Cylinder, surface area of the cylinder, volume of the cylinder, right cylinder, 72, 36, 45, 90, height, radius depth.
