RS Aggarwal Test: Surface Areas & Volumes - Class 10 MCQ

Given, a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm.

We have to find the quantity of water that flows out of the cylindrical cup.

We know that when the marble is put inside the cylindrical cup full of water the volume of water displaced is equal to the volume of the marble.

So, volume of water that flows out = volume of the marble

Volume of sphere = (4/3)πr³

Given, radius = 2.1 cm

So, volume of marble = (4/3)(22/7)(2.1)³

= 38.808 cm³

Therefore, the volume of the water that flows out is 38.8 cm³

Answer: (c) Remains unchanged

Explanation: If we change the shape of a three-dimensional object, the volume of the new shape will be same.

Answer: b) 120π cm²

To find the number of bricks used to construct the wall, we will follow these steps:

Step 1: Calculate the Volume of the Wall
The volume V of a cuboid is given by the formula:
V=Length×Breadth×Height
For the wall, the dimensions are:
- Length = 270 cm
- Breadth = 300 cm
- Height = 350 cm

Calculating the volume:
Vwall=270cm×300cm×350cm
Vwall=28350000cm³

Step 2: Adjust for Mortar
Since 18 of the volume is covered by mortar, the volume occupied by bricks is:
Vbricks=Vwall×78
Calculating the volume occupied by bricks:
Vbricks=28350000×78=24806250cm³

Step 3: Calculate the Volume of One Brick
The dimensions of one brick are:
- Length = 22.5 cm
- Breadth = 11.25 cm
- Height = 8.75 cm

Using the volume formula for the brick:
Vbrick=22.5cm×11.25cm×8.75cm
Calculating the volume of one brick:
Vbrick=22.5×11.25×8.75=2214.84375cm³

Step 4: Calculate the Number of Bricks
To find the number of bricks used, divide the volume occupied by bricks by the volume of one brick:
N=VbricksVbrick
Calculating the number of bricks:
N=248062502214.84375≈11200

Final Answer
The number of bricks used to construct the wall is 11200.

Answer: (b) 10a²

Explanation:

The total surface area of a cube having side a = 6a²

If two identical faces of side a are joined together, then the total surface area of the cuboid so formed is 10a².