NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.1
Question 11

Question.  11

A wall of dimensions 270 cm \(\times\) 300 cm \(\times\) 350 cm is built with bricks of size 22.5 cm \(\times\) 11.25 cm \(\times\) 8.75 cm. If \(\dfrac{1}{8}\) of the space is covered by mortar, the number of bricks used is

(A)

11100

(B)

11200

(C)

11000

(D)

11300

Detailed Answer with Explanation:

Step 1: Find the volume of one brick.

Each brick has dimensions: \(22.5\,\text{cm} \times 11.25\,\text{cm} \times 8.75\,\text{cm}\).

So, volume of one brick = \(22.5 \times 11.25 \times 8.75 = 2214.84375\,\text{cm}^3\).

Step 2: Find the total volume of the wall (without considering mortar).

Wall dimensions = \(270\,\text{cm} \times 300\,\text{cm} \times 350\,\text{cm}\).

Total wall volume = \(270 \times 300 \times 350 = 28,350,000\,\text{cm}^3\).

Step 3: Adjust for mortar.

We are told \(\tfrac{1}{8}\) of the volume is filled with mortar, not bricks.

So, fraction available for bricks = \(1 - \tfrac{1}{8} = \tfrac{7}{8}\).

Usable volume = \(\tfrac{7}{8} \times 28,350,000 = 24,806,250\,\text{cm}^3\).

Step 4: Find how many bricks can fit in this usable volume.

Number of bricks = \(\dfrac{24,806,250}{2214.84375} \approx 11200\).

Final Answer: The number of bricks used is 11200.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 12: Surface Areas & Volumes – Exercise 12.1 | Detailed Answers