Question

6. Find the volume, lateral surface area and the total surface area of the cuboid whose
dimensions are:
(1) length = 22 cm, breadth=12 cm and the height = 7.5 cm
(ii) length = 24 m, breadth = 25 cm and the height = 6 m

Answer 1

To Find:-

The volume, lateral surface area and the total surface area of the cuboid whose dimensions are:-

• (i) length = 22 cm, breadth = 12 cm, height = 7.5 cm
• (ii) length = 24 m, breadth = 25 cm, height = 6 m

Solution:-

(i) length = 22 cm

breadth = 13 cm

height = 7.5 cm

Firstly let us calculate the volume of the cuboid.

We know,

• Volume of cuboid = Length × breadth × height

Therefore,

Volume = 22 × 12 × 7.5

⇒ Volume = 1980 cm³

∴ Volume of the cuboid is 1980 cm³.

Now,

Let us calculate lateral surface area.

We know,

• LSA of a cuboid = 2(Length + Breadth) × Height

Therefore,

LSA = 2(22 + 12) × 7.5

⇒ LSA = 2 × 34 × 7.5

⇒ LSA = 510 cm²

∴ Lateral Surface Area of the cuboid is 510 cm².

Now,

Let us calculate the total surface area of the cuboid.

We know,

• TSA of cuboid = 2(LB + BH + HL)
• Where L = Length, B = Breadth and H = Height

Hence,

TSA = 2[(22 × 12) + (12 × 7.5) + (7.5 × 22)]

⇒ TSA = 2 [264 + 90 + 165]

⇒ TSA = 2 × 519

⇒ TSA = 1038 cm²

∴ Total Surface Area of the cuboid is 1038 cm².

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(ii) Length = 24 m

Breadth = 25 cm = 0.25 m

Height = 6 m

Volume = L × B × H

⇒ Volume = 24 × 0.25 × 6

⇒ Volume = 36 m²

∴ Volume of the cuboid is 36 m²

LSA = 2(L + B) × Height

⇒ LSA = 2(24 + 0.25) × 6

⇒ LSA = 2 × 24.25 × 6

⇒ LSA = 291 m²

∴ Lateral Surface Area of the cuboid is 291 m².

TSA = 2(LB + BH + HL)

⇒ TSA = 2[(24 × 0.25) + (0.25 × 6) + (6 × 24)]

⇒ TSA = 2[6 + 1.5 + 144]

⇒ TSA = 2 × 151.5

⇒ TSA = 303 m²

∴ Total Surface Area of the cuboid is 303 m².

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Answer 2

(i) length = 22 cm, breadth=12 cm and the height = 7.5 cm

Answer -

➺ Volume:-

• Volume of cuboid = l × b × h

So,

= l × b × h

= 22cm × 12cm × 7.5cm

= 1980cm³

➺ Lateral Surface Area:-

• Lateral surface area of cuboid = 2h(l + b)

So,

= 2h(l+b)

= 2×7.5(22cm+12cm)

= 15(34cm)

= 510cm²

➺ Total Surface Area:-

• Total surface area of cuboid = 2(lb+bh+hl)

So,

= 2(lb+bh+hl)

= 2(22×12 + 12×7.5 + 7.5×22)cm²

= 2(264+90+165)cm²

= 2(519)

= 1038cm²

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(ii) length = 24 m, breadth = 25 cm and the height = 6 m

Answer -

➺ Volume:-

• Volume of cuboid = l × b × h

So,

= l × b × h

= 24m × 25cm × 6m

= 2400cm × 25cm × 600cm

= 36000000cm³

➺ Lateral Surface Area:-

• Lateral surface area of cuboid = 2h(l + b)

So,

= 2h(l+b)

= 2×6m(24m+25cm)

= 2×600cm(2400cm+25cm)

= 1200cm(2425cm)

= 2910000cm²

➺ Total Surface Area:-

• Total surface area of cuboid = 2(lb+bh+hl)

So,

= 2(lb+bh+hl)

= 2(24m×25cm + 25cm×6m +6m×24m)

= 2(2400cm×25cm + 25cm×600cm + 600cm×2400cm)

= 2(60000cm² + 15000cm² + 1440000cm²)

= 2(1515000cm²)

= 3030000cm²

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Related information:-

Here,

• l = length of cuboid
• b = breadth of cuboid
• h = height of cuboid

Formula:-

• Volume of cuboid = l × b × h

• Lateral surface area of cuboid = 2h(l+b)

• Total surface area of cuboid = 2(lb+bh+hl)

I've converted the m(meter) unit into cm(centimetre) by multiplying it from 100(because 1m=100cm).