Question

A cuboid has a capacity of 7 and a half litres calculate the height of the cuboid if the lengtht is 25cm and the width is 20cm

Answer 1

To calculate the height of the cuboid, we can use the formula for the volume of a cuboid:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

We know that the volume (capacity) of the cuboid is \(7.5\) liters. We need to convert this volume to cubic centimeters, since the length and width are given in centimeters.

1 liter = 1000 cubic centimeters, so:

\[
7.5 \text{ liters} = 7.5 \times 1000 \text{ cm}^3 = 7500 \text{ cm}^3
\]

Now, substituting the known values into the volume equation:

\[
7500 \text{ cm}^3 = 25 \text{ cm} \times 20 \text{ cm} \times \text{Height}
\]

Calculating the product of the length and width:

\[
25 \text{ cm} \times 20 \text{ cm} = 500 \text{ cm}^2
\]

Now, we can substitute this value back into the volume equation:

\[
7500 \text{ cm}^3 = 500 \text{ cm}^2 \times \text{Height}
\]

To find the height, we divide both sides by \(500 \text{ cm}^2\):

\[
\text{Height} = \frac{7500 \text{ cm}^3}{500 \text{ cm}^2} = 15 \text{ cm}
\]

Thus, the height of the cuboid is \( \boxed{15} \) cm.