Calculate the volumes of the cylinder, rectangular prism, and hexagonal prism shown in the image.

Question

ScanSolve AI Tutor · Accepted Answer

here are the calculations for the volumes of the shapes:

Cylinder (top left)

Identify the shape and given dimensions.
The shape is a cylinder.
The height of the cylinder is $h = 10$ cm.
The radius or diameter of the circular base is not provided in the image.
State the formula for the volume of a cylinder.
The volume of a cylinder is given by the formula:
$V = \pi r^2 h$
where $r$ is the radius of the base and $h$ is the height.
Conclude due to missing information.
Since the radius $r$ is not given, the numerical volume cannot be calculated.

Shape F: Rectangular Prism (Cuboid)
Identify the shape and given dimensions.
The shape is a rectangular prism (cuboid).
The length is $L = 8$ m.
The width is $W = 5$ m.
The height is $H = 5$ m (inferred from the tick marks matching the width).
State the formula for the volume of a rectangular prism.
The volume of a rectangular prism is given by the formula:
$V = L \times W \times H$
Substitute the values and calculate the volume.
$V = 8 \text{ m} \times 5 \text{ m} \times 5 \text{ m}$ $V = 200 \text{ m}^3$
The volume of Shape F is $\boxed{\text{200 m}^3}$ .

Shape G: Hexagonal Prism
Identify the shape and given dimensions.
The shape is a hexagonal prism.
The height of the prism is $H_{\text{prism}} = 5$ cm.
The base is a regular hexagon with side length $s = 6$ cm.
Calculate the area of the regular hexagonal base.
The area of a regular hexagon with side length $s$ is given by:
$A_{\text{base}} = \frac{3\sqrt{3}}{2} s^2$
Substitute

Answer