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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 7 Mensuration Ex 7.2

Question 1.

Find the total surface area and the lateral surface area of a cuboid whose dimensions are

(i) length = 20 cm,

breadth = 15 cm,

height = 8 cm

Solution:

(i) (a) Total surface Area of cuboid = 2(lb + bh + hl) sq. units

= 2(20 × 15 + 15 × 8 + 8 × 20)

= 2(300 + 120 + 160) = 2 × 580

(b) Lateral surface area of a cuboid = 2h(l + b) sq. units

= 2 × 8 (20 + 15) = 16 × 35 = 560 cm^{2}

Question 2.

The dimensions of a cuboidal box are 6 m × 400 cm × 1.5 m. Find the cost of painting its entire outer surface at the rate of ₹ 22 per m^{2}

Solution:

l × b × h = 6 m × 400 cm × 1.5 m

l = 6m,

b = 4 m,

h = 1.5 m

∴ Total surface area of the cuboid = Outer surface area

= 2(lb + bh + hl) = 2((6 × 4) + (4 × 1.5) + (1.5 × 6))

= 2(24 + 6 + 9) = 2(39) m^{2}

Cost of painting 1 m^{2} = ₹ 22

Cost of painting 78 m^{2} = 78 × 22 = ₹ 1716

Question 3.

The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of ₹ 8.50 per m^{2}.

Solution:

Dimensions of a hall 10m × 9m × 8m

l = 10 m

b = 9m

h = 8 m

White washing to be done for the area of the surface

= 2 (lh + bh) + lb

= 2 (10 × 8 + 9 × 8) + 10 × 9

= 2 (80 + 72) + 90 = 2 × 152 + 90

= 304 + 90 = 394 m^{2}

Cost of white washing per m^{2} = ₹ 8.50

Cost of white washing 394 m^{2} = 394 × 8.50

Total cost = ₹ 3349

Question 4.

Find the TSA and LSA of the cube whose side is

(i) 8 m

(ii) 21 cm

(iii) 7.5 cm

Solution:

(i) side of a cube = 8m

TSA of the cube = 6a^{2} = 6 × 64 = 384 m^{2}

LSA of the cube = 4a^{2}= 4 × 64 = 256 m^{2}

(ii) side a 21 cm

TSA = 6a^{2} = 6 × 21 × 21 = 2646 cm^{2}.

LSA = 4a^{2} = 4 × 21 × 21 = 1764 cm^{2}.

(iii) side a = 7.5 cm

TSA = 6a^{2} = 6 × 7.5 × 7.5 cm^{2} = 337.5 cm^{2}

LSA = 4a^{2} = 4 × 7.5 × 7.5 cm^{2} = 225 cm^{2}

Question 5.

If the total surface area of a cube is 2400 cm^{2} then, find its lateral surface area.

Solution:

Question 6.

A cubical container of side 6.5 m is to be painted on the entire outer surface. Find the area to be painted and the total cost of painting it at the rate of ₹ 24 per m^{2}.

Solution:

a = 6.5 m

6a^{2} = 6 × 6.5 × 6.5 = 253.5 m^{2}

Area to be painted = 253.5 m^{2}

Cost of painting 1 m^{2} = ₹ 24

∴ Cost of painting 253.5 m^{2} = 253.5 × 24 = ₹ 6084

Question 7.

Three identical cubes of side 4 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid.

Solution:

a = 4 cm

TSA of the cuboid = 2(lb + bh + hl)

l = 12 cm

b = 4 cm

h = 4 cm

∴ TSA = 2(12 × 4 + 4 × 4 + 4 × 12)

= 2(48 + 16 + 48) = 2 × 112 = 224 cm^{2}

LSA = 2h(l + b) = 2 × 4(12 + 4) = 8 × 16 = 128 cm^{2}