Maths Case study (4 Marks)

Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The top of the hut is a cone with radius 4 m and height 1 m. It is made of economical material. The loor of the tent is covered with rugs.
The total height of the tent is 4.5 m. The cuboidal part of the tent is 6 m long and 5 m wide.
1. What is the outer surface area (in m²) of the hut?
  A. 77
  B. 77+4π√17
  C. 137+4π√17
  D. 137+4π(4+√17)
2. The length and width of a rug used for the loor are 2.6 m and 2 m respectively.
What is the minimum number of rugs required to cover the loor of the tent house? 

A company manufactures wooden boxes. Given below is the picture of an open wooden box. 

The height of the box is 25 cm.
7. What is the surface area (in cm²) of the box?
  A. 3500
  B. 4700
  C. 5900
  D. 30000
8. A shopkeeper store cubes in it.
The side length of one cube is 9 cm.
What would be the maximum number of cubes the shopkeeper can store in a box? (All cubes should be inside the box.)
9. Rajan packs a football into a cubical cardboard box. The radius of the football is 11 cm. Rajan keeps a margin of 1 cm from all the sides of the box while packing.
What is the side length of the cardboard box? 
  A. 11 cm
  B. 20 cm
  C. 22 cm
  D. 24 cm

This is the picture of a gas balloon illed with helium gas.

This balloon has 18 faces that are square in shape and 8 equilateral faces that are triangular.
3. Which of the following is the net of the balloon?

4. The side length of the square is 20 cm. What is the total surface area of the balloon?

Raghav bought this planter.

The radius of the rim is 14 cm. The curved surface area of the planter is 1848 cm².
5. What is the height of the planter?
6. What is the volume of the planter?

Read the passage given below and answer any four questions:
Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length 4m, width 2m and the height 3m as shown in the following figure.
The room was separate at the roof of the house. The dimensions of the bricks used are: 25cm × 10cm × 5cm.

1. Total how many bricks will be required? (1m³ =1000000cm³):

1. 30000
2. 40000
3. 28800
4. 27000

2. How many bricks will be used on both walls along the length (length = 4m)?

1. 19200
2. 20200
3. 18800
4. 17000

3. How many bricks will be used on both walls along the width (width = 3m)?

1. 19200
2. 9600
3. 10000
4. 15000

4. What is the volume of the room?

1. 24m³
2. 12m³
3. 20m³
4. 15m³

5. What is the area of the floor?

1. 10m²
2. 12m²
3. 8m²
4. 8m³

Read the Source/ Text given below and answer any four questions:
Veena planned to make a jewellery box to gift her friend Reeta on her marriage. She made the jewellery box of wood in the shape of a cuboid. The jewellery box has the dimensions as shown in the figure below. The rate of painting the exterior of the box is Rs. 2 per cm². After making the box she took help from his friends to decorate the box.
The blue colour was painted by Deepak, Black by Suresh, green by Harsh and the yellow was painted by Naresh.

1. What is the volume of the box?

1. 24000cm³
2. 1200cm³
3. 800cm³
4. 600cm³

2. How much area did Suresh paint?

1. 24000cm²
2. 1200cm²
3. 800cm²
4. 600cm²

3. How much area did Deepak paint?

1. 24000cm²
2. 600cm²
3. 800cm²
4. 1200cm²

4. What amount did Harsh charge?

1. Rs. 800
2. Rs. 1200
3. Rs. 1600
4. Rs. 2000

5. What amount did Veena pay for painting:

1. Rs. 2600
2. Rs. 5200
3. Rs. 5000
4. Rs. 6000

Read the passage given below and answer these questions:
Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying 300m² cloth with them. As shown in the figure they made the tent with height 10m and diameter 14m. The remaining cloth was used for the floor.

1. How much Cloth was used for the floor?

1. 31.6m²
2. 16m²
3. 10m²
4. 20m²

2. What was the volume of the tent?

1. 300m³
2. 160m³
3. 513.3m³
4. 500m³

3. What was the area of the floor?

1. 50m²
2. 100m²
3. 150m²
4. 154m²

4. What was the total surface area of the tent?

1. 400m²
2. 422.4m²
3. 300m²
4. 400m²

5. What was the latent height of the tent?

1. 12m
2. 12.2m
3. 15m
4. 17m

Read the passage given below and answer these questions:
Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius R = 7cm and height 10cm. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from A to B equal to 3.40cm.

1. What is the approximate radius of the sphere?

1. 7cm
2. 5cm
3. 4cm
4. 3cm

2. What is the volume of the cylinder?

1. 700cm³
2. 500cm³
3. 1540cm³
4. 2000cm³

3. What is the volume of the sphere?

1. 700cm³
2. 600cm³
3. 500cm³
4. 523.8cm³

4. How many litres water can be filled in the full container? ( Take 1 litre = 1000cm³):

1. 1.50
2. 1.44
3. 1.54
4. 2

5. What is the surface area of the sphere?

1. 314.3m²
2. 300m²
3. 400m²
4. 350m²

Read the Source/ Text given below and answer these questions:

In Agra in a grinding mill, there were installed 5 types of mills. These mills used steel balls of radius 5mm, 7mm,10mm, 14mm and 16mm respectively. All the balls were in the spherical shape. For repairing purpose mills need 10 balls of 7mm radius and 20 balls of 3.5mm radius. The workshop was having 20000mm³ steel. This 20000mm³ steel was melted and 10 balls of 7mm radius and 20 balls of 3.5mm radius were made and the remaining steel was stored for future use.
Answer the following questions:

1. What was the volume of 10 balls of radius 7mm?

1. 14373.3mm³
2. 14000mm³
3. 7000mm³
4. 20000mm³

2. What was the volume of 20 balls of radius 3.5mm?

1. 2000mm³
2. 1800mm³
3. 1796.6mm³
4. 3593.3mm³

3. How much steel was kept for future use?

1. 1250mm³
2. 2033.3mm³
3. 1300mm³
4. 2200mm³

4. What was the surface area of one ball of 7mm radius?

1. 600mm²
2. 616mm²
3. 308mm²
4. 400mm²

5. What was the surface area of one ball of 3.5mm radius?

1. 600mm²
2. 616mm²
3. 308mm²
4. 154mm²