What is the height of a cuboid whose cross sectional area is 48cm² and volume is 216cm²

Question

Create an illustration of a mathematical concept. Detail an idealized, clean room with white walls. The main focus of the image is a large cuboid, standing upright on a polished wooden table. The cuboid is transparent, so we can see its inner part. Make it look as if it's made of glass. Highlight the width and length represented with dotted lines, indicating that the cross-sectional area is 48cm². A similar dotted line should demonstrate the height of the cuboid. To represent the volume, include small, loosely packed cubes, each with a volume of 1cm³, filling up the entire glass cuboid, indicating its total volume is 216cm³.

What is the height of a cuboid whose cross sectional area is 48cm² and volume is 216cm²

Answer 1

48 h = 216

h = 4.5

Answer 2

Well, if the cross-sectional area of the cuboid is 48cm² and the volume is 216cm², then it sounds like you have a magical cuboid on your hands! But unfortunately, I think there may be a little mix-up with the units here. The cross-sectional area is typically measured in square units (cm²), while the volume is measured in cubic units (cm³). So, I'm afraid I can't give you a meaningful answer to your question. But hey, at least we had some fun along the way!

Answer 3

To find the height of the cuboid, we will use the formula for volume of a cuboid:

Volume = length × width × height

Given that the volume is 216 cm³, we can express this mathematically:

216 = length × width × height

We are also given that the cross-sectional area is 48 cm². The cross-sectional area of a rectangle is equal to the length multiplied by the width, so:

48 = length × width

Now we have two equations with two variables (length and width), and we can solve them simultaneously to find the values for length and width.

To do this, we need to find a factor pair of 48, because the numbers multiplied together should give a product of 48. By trial and error, we can find that 6 × 8 = 48. So, we can set length = 6 cm and width = 8 cm.

Now let's substitute these values into the volume equation:

216 = 6 × 8 × height

Simplifying the equation:

216 = 48 × height

Dividing both sides of the equation by 48:

height = 216 / 48

height = 4.5 cm

Therefore, the height of the cuboid is 4.5 cm.

Answer 4

To find the height of a cuboid given its cross-sectional area and volume, we can use the formula:

Volume = Cross-sectional area x Height

In this case, we are given the cross-sectional area as 48cm² and the volume as 216cm³.

So, let's plug these values into the formula:

216cm³ = 48cm² x Height

To solve for the height, we need to isolate the height variable. We can do this by dividing both sides of the equation by 48cm²:

216cm³ / 48cm² = Height

Simplifying the left side of the equation:

4.5cm = Height

Therefore, the height of the cuboid is 4.5cm.