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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 7 Mensuration Additional Questions

Exercise 7.1

Question 1.

Using Heron’s formula, find the area of a triangle whose sides are 41 m, 15 m, 25 m.

Solution:

Question 2.

Find the area of an equilateral triangle whose perimeter is 150 m.

Solution:

3a = 150

Question 3.

Find the area of a quadrilateral whose sides are PQ = 15 cm, QR = 8 cm, RS = 25 cm, PS = 12 cm and LQ = 90°

Solution:

Exercise 7.2

Question 1.

Find the TSA and LSA of a cuboid whose length, breadth and height are 10 cm, 12 cm and 14 cm respectively.

Solution:

TSA = 2 (lb + bh + Ih)

= 2 (10 × 12 + 12 × 14 + 10 × 14) = 2 (120 + 168 + 140) = 856 cm^{2}

LSA = 2 (bh + Ih) = 2 (12 × 14 + 10 × 14) = 2 (168 + 140) =2 (308) = 616 cm^{2}

Question 2.

A cuboid has total surface area of 40 m^{2} and its lateral surface area is 26 m^{2}. Find the area of its base.

Solution:

Question 3.

Find the surface area of a cube whose edge is

(i) 27 cm

(ii) 3 cm

(iii) 6 cm

(iv) 2.1 cm

Solution:

(i) TSA = 6a^{2} = 6 × 27^{2} = 6 × 729 = 4374 cm^{2}

(ii) TSA = 6a^{2} = 6 × 3^{2} = 54 cm^{2}

(iii) TSA = 6a^{2} = 6 × 6^{2} = 6 × 36 = 216 cm^{2}

(iv) TSA = 6a^{2} = 6 × 2.1^{2} = 6 × 4.41 = 26.46 cm^{2}

Exercise 7.3

Question 1.

Find the volume of a cube whose surface area is a 96 cm^{2}.

Solution:

6a^{2} = 96 cm^{2}

a = 6

Volume = a^{3} = 6^{3} = 36 × 6 = 216 cm^{3}

Question 2.

The volume of a cuboid is 440 cm^{3} and the area of its base is 88 cm^{2}, find its height.

Solution:

l × b × h = 440 cm^{3}

Question 3.

How many 3 metre cubes can be cut from a cuboid measuring 18 m × 12 m × 9 m?

Solution:

Question 4.

The outer dimensions of a closed wooden box are 10 cm by 8 cm by 7 cm. Thickness

of the wood is 1 cm^{3}. Find the total cost of wood required to make box if 1 cm^{3} of wood costs ₹ 2.00?

Solution:

Volume of wood = 12 × 10 × 9 – 10 × 8 × 7 = 1080 – 560 = 520 cm^{3} × 2.00 = ₹ 1040