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1. Find the height of a rectangular pillar if its volume is 24,192 cubic inches, and its length and breadth are 18 inches and 14 inches, respectively.

2. (a) Find the volume of a rectangular container with a height of 9 ft and a base area of 150 ft².

(b) Find the volume of a rectangular A4 paper box with a height of 12 cm and a base area of 36 cm².

Answer :

Sure! Let's solve each part of the question step-by-step:

1. Finding the height of a rectangular pillar:

- We know the volume of the pillar is 24,192 cubic inches.
- The length of the pillar is 18 inches.
- The breadth of the pillar is 14 inches.

To find the height, we use the formula for the volume of a rectangular prism:

[tex]\[
\text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height}
\][/tex]

Rearrange the formula to solve for height:

[tex]\[
\text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Breadth}}
\][/tex]

Substituting the given values:

[tex]\[
\text{Height} = \frac{24,192}{18 \times 14} = \frac{24,192}{252}
\][/tex]

Calculating gives:

[tex]\[
\text{Height} = 96 \text{ inches}
\][/tex]

2. Finding the volume of a rectangular container:

- The height of the container is 9 feet.
- The base area of the container is 150 square feet.

The volume of the container can be found using:

[tex]\[
\text{Volume} = \text{Base Area} \times \text{Height}
\][/tex]

Substituting the given values:

[tex]\[
\text{Volume} = 150 \times 9
\][/tex]

Calculating gives:

[tex]\[
\text{Volume} = 1,350 \text{ cubic feet}
\][/tex]

3. Finding the volume of a rectangular A4 paper box:

- The height of the box is 12 cm.
- The base area of the box is 36 cm².

The volume of the box is calculated the same way as the container:

[tex]\[
\text{Volume} = \text{Base Area} \times \text{Height}
\][/tex]

Substituting the given values:

[tex]\[
\text{Volume} = 36 \times 12
\][/tex]

Calculating gives:

[tex]\[
\text{Volume} = 432 \text{ cubic cm}
\][/tex]

So, the final answers are:
- The height of the rectangular pillar is 96 inches.
- The volume of the rectangular container is 1,350 cubic feet.
- The volume of the rectangular A4 paper box is 432 cubic cm.

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Rewritten by : Barada