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**Exercise 11.3**

**Question 1. **There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

**Solution: **Total surface area of the cuboid (a) = 2[lb + bh + hl]

Total surface area of the cuboid (b)

Since the total surface area of the second (b) is more.

âˆ´ Cuboid (a) will require lesser material.

**Question 2.** A suitcase with measures 80 cm *48 cm * 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

**Solution:** Total surface area of a suitcase

âˆ´ Total S.A. of 100 suitcases = 100* 13824 cm2 = 1382400 cm^{2}

Surface area of 1 m of tarpaulin = 100 cm * 96 cm = 9600 cm^{2}

i.e. 1 m of tarpaulin can cover 9600 cm2 surface

âˆ´ 1382400/9600 metres of tarpaulin will cover the total surfaces of 100 suitcases

i.e. 1382400/9600 or 144 metres of tarpaulin will be required to cover 100 suitcases.

**Question 3.** Find the side of a cube whose surface area is 600 cm^{2}.

**Solution:** Let the side be x cm.

âˆ´ Total S.A. of the cube = 6 * x^{2} cm^{2}

But the S.A. of the cube = 600 cm^{2}

âˆ´ 6x^{2} = 600

or x^{2} = 600/6 = 100

or x^{2 }= 10^{2}â‡’x = 10

âˆ´ The required side of the cube = 10 cm

**Question 4.** Rukhsar painted the outside of the cabinet of measure 1 m * 2 m * 1.5 m. How much surface area did she cover if she painted all except bottom of the cabinet?

**Solution:** Total surface area = 2[lb * bh + hl]

But bottom is not painted.

i.e. Area not painted = lb

âˆ´ Total S.A. to be painted = 2(bh + hl) + bh

**Question 5**. Daniel is painting the walls and ceiling of a cuboidal hall with length breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m2 of area is painted. How many cans of paint will she need to paint the room?

**Solution: **Area to be painted = [Area of 4-walls] + Area of ceiling

= 2[Perimeter * Height] + l * b

= 2[(15 + 10) * 7] + 15 * 10 m^{2}

= 2[25 * 7] + 150 m^{2}

= 2 * 175 + 150 m^{2}

350 + 150 m^{2} = 500 m^{2}

Since 1 can of paint covers 100 m^{2} area.

âˆ´ Number of cans required = 500/100 = 5

**Question 6.** Describe how the two figures at the right are alike and how they are different. Which box has larger surface area?

**Solution:** Similarity: Both have the same height.

Difference: Cylinder has curved and circular surfaces.

Cube: All faces are identical squares.

Lateral surface area of the cylinder = 2Ï€rh

Lateral surface area of the cube = 4l^{2}

= 4 * (7 * 7) cm^{2}

= 4 * 49 cm2 = 196 cm^{2}

Obviously the cubical box has larger surface area.

**Question 7. **A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

**Solution:** Here, r = 7 m and h = 3 m

âˆ´ Total surface area = 2Ï€r(r + h)

Thus, 440 m^{2} metal is required.

**Question 8.** The lateral surface area of a hollow cylinder is 4224 cm^{2}. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet.

**Solution:** âˆµ Lateral surface area of a cylinder = 4224 cm^{2}

and let length of the rectangular sheet = l cm

33 * l = 4224

l = 4224/33 = 128 cm

Now perimeter of the rectangular sheet = 2 [Length + Breadth]

= 2 [128 cm + 33 cm]

= 2 *161 cm = 322 cm

**Question 9.** A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

**Solution: **The road roller is a cylinder.

Radius = 84/2 cm = 42 cm

Length (h) = 1 m = 100 cm

âˆ´ Lateral surface area = 2Ï€rh

âˆ´ Area levelled by the roller in 1 revolution = 26400 cm^{2}

or Area levelled in 750 revolutions = 750 * 26400 cm^{2}

Thus, the required area of the road = 1980 m^{2}

**Question 10. **A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container as shown in the figure. If the label is placed 2 cm from top and bottom, what is the area of the label?

**Solution: **The label is in the shape of a cylinder having

Radius = 14/2 cm = 7 cm and Height = (2 + 2) cm less than the height of the container

or Height of the label = 20 cm â€“ [2 + 2] cm = 16 cm [âˆµ The label is placed 2 cm from top and bottom.]

âˆ´ Area of the label = 2Ï€rh

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