## RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area

**Exercise 13A**

**Question 1:**

(i) length =12cm, breadth = 8 cm and height = 4.5 cm

∴ Volume of cuboid = l x b x h

= (12 x 8 x 4.5) cm^{3}= 432 cm^{3}

∴ Lateral surface area of a cuboid = 2(l + b) x h

= [2(12 + 8) x 4.5] cm^{2}

= (2 x 20 x 4.5) cm^{2} = 180 cm^{2}

∴ Total surface area cuboid = 2(lb +b h+ l h)

= 2(12 x 8 + 8 x 4.5 + 12 x 4.5) cm^{2}

= 2(96 +36 +54) cm^{2}

= (2 x186) cm^{2}

= 372 cm^{2}

(ii) Length 26 m, breadth =14 m and height =6.5 m

∴ Volume of a cuboid = l x b x h

= (26 x 14 x 6.5) m^{3}

= 2366 m^{3}

∴ Lateral surface area of a cuboid =2 (l + b) x h

= [2(26+14) x 6.5] m^{2}

= (2 x 40 x 6.5) m^{2}

= 520 m^{2}

∴ Total surface area = 2(lb+ bh + lh)

= 2(26 x 14+14 x6.5 +26 x6.5)

= 2 (364+91+169) m^{2}

= (2 x 624) m2= 1248 m^{2}.

(iii) Length = 15 m, breadth = 6m and height = 5 dm = 0.5 m

∴ Volume of a cuboid = l x b x h

= (15 x 6 x 0.5) m3=45 m^{3}.

∴ Lateral surface area = 2(l + b) x h

= [2(15 + 6) x 0.5] m^{2}

= (2 x 21×0.5) m2=21 m^{2}

∴ Total surface area =2(lb+ bh + lh)

= 2(15 x 6 +6 x 0.5+ 15 x 0.5) m^{2}

= 2(90+3+7.5) m^{2}

= (2 x 100.5) m^{2}

=201 m^{2}

(iv) Length = 24 m, breadth = 25 cm =0.25 m, height = 6m.

∴ Volume of cuboid = l x b x h

= (24 x 0.25 x 6) m^{3}.

= 36 m^{3}.

∴ Lateral surface area = 2(l + b) x h

= [2(24 +0.25) x 6] m^{2}

= (2 x 24.25 x 6) m^{2}

= 291 m^{2}.

∴ Total surface area =2(lb+ bh + lh)

=2(24 x 0.25+0.25x 6 +24 x 6) m^{2}

= 2(6+1.5+144) m^{2}

= (2 x151.5) m^{2 }

=303 m^{2}.

**Read More:**

- Surface Area and Volume of a Cuboid
- Surface Area and Volume of a Cube
- Surface Area of a Sphere and a Hemisphere

**Question 2:**

Length of Cistern = 8 m

Breadth of Cistern = 6 m

And Height (depth) of Cistern =2.5 m

∴ Capacity of the Cistern = Volume of cistern

∴ Volume of Cistern = (l x b x h)

= (8 x 6 x2.5) m^{3}

=120 m^{3}

Area of the iron sheet required = Total surface area of the cistem.

∴ Total surface area = 2(lb +bh +lh)

= 2(8 x 6 + 6×2.5+ 2.5×8) m^{2}

= 2(48 + 15 + 20) m^{2}

= (2 x 83) m2=166 m^{2}

**Question 3:**

Length of a room =9m,

Breadth of a room = 8m

And height of room = 6.5 m

∴ Area of 4 walls = Lateral surface area

= 2 (l+ b) x h

= [2 (9+8) x 6.5] m^{2}

= (2 x 17 x 6.5) m^{2}

=221 m^{2}

∴ Area not be whitewashed = (area of 1 door) + (area of 2 windows)

= (2 x 1.5) m^{2} + (2 x 1.5 x 1) m^{2}

= 3m^{2 }+ 3m^{2 }=6m^{2}

∴ Area to be whitewashed = (221-6) m^{2} =215 m^{2}

∴ Cost of whitewashing the walls at the rate of Rs.6.40 per

Square meter = Rs. (6.40 x 215) = Rs. 1376

**Question 4:**

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**Question 20:**

**Exercise 13B**

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**Exercise 13C**

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**Exercise 13D**

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**Question 20:**

**Question 21:**

**Question 22:**

**Question 23:**