6th grade Q4

Here is how you can solve problems involving volumes of solids:

1. Understand the Shape and Formula: Identify the shape of the solid (e.g., cube, rectangular prism, cylinder, cone, sphere) and recall the corresponding formula for volume.
2. Identify Given Dimensions: Look for the dimensions necessary to use the formula. This could be length, width, height, radius, etc.
3. Substitute and Solve: Plug the dimensions into the formula and solve for volume.

Example 1:

Imagine you have a rectangular prism-shaped aquarium that needs to be filled with water. The aquarium has a length of 100 units, a width of 40 units, and a height of 60 units. You want to know how much water is needed to fill the aquarium completely.

To find the volume of a rectangular prism, you use the formula:

where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

First identify the dimensions of your aquarium:

• Length ($l$) = 100 units
• Width ($w$) = 40 units
• Height ($h$) = 60 units

Then substitute the dimensions into the formula and calculate the volume:

Answer:

The volume of the aquarium is 240 000 cubic units.

-----

Example 2:

Imagine you have a soda can shaped like a cylinder. It needs to be filled with soda, and you want to know how much soda it can hold. The soda can has a height of 10 units and a radius of 2 units.

To find the volume of a cylinder, you use the formula:

where $V$ is the volume, $r$ is the radius, and $h$ is the height.

First identify the dimensions of your can:

• Radius ($r$) = 2 units
• Height ($h$) = 10 units

Then substitute the dimensions into the formula and calculate the volume:

To get a numerical value, use the approximation $\pi \approx 3.14$

Answer:

The volume of the soda can is approximately 125.6 cubic units.