Question

The lateral surface area of a cuboid is 330 cm². If the length and width of the cuboid are 10.5 cm and
4.5 cm respectively,
find the height of the cuboid.​

Answer 1

Answer:

Page No 555:

Question 1:

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

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

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

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

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

ANSWER:

(i)

Here, l = 12 cm, b = 8 cm, h = 4.5 cm

Volume of the cuboid = l×b×h

=(12×8×4.5) cm3= 432 cm3

Total Surface area = 2(lb + lh+ bh)

=2(12×8 + 12×4.5 +8×4.5) cm2=2(96 +54 + 36) cm2=2× 186 cm2=372 cm 2

Lateral surface area = 2(l+b)×h

=[2(12+8)×4.5] cm2=[2(20)×4.5] cm2=40×4.5 cm2=180 cm2

(ii)

Here, l = 26 m; b = 14 m; h =6.5 m

Volume of the cuboid = l×b×h

=(26×14×6.5)m3=2366 m3

Total surface area = 2(lb + lh+ bh)

=2(26×14+26×6.5+6.5×14) m2=2(364+169+91) m2=2×624 m2=1248 m2

Lateral surface area = 2(l+b)×h

=[2(26+14)×6.5] m2=[2×40×6.5] m2=520 m2

(iii)

Here, l = 15 m; b = 6 m; h = 5 dm = 0.5 m

Volume of the cuboid = l×b×h

=(15×6×0.5) m3=45 m3

Total surface area = 2(lb + lh+ bh)

=2(15×6+15×0.5+6×0.5) m2=2(90+7.5 +3) m2=2×100.5 m2= 201m2

Lateral surface area = 2(l+b)×h

=[2(15+6)×0.5] m2=[2×21×0.5] m2=21 m2

(iv)

Here, l = 24 m; b = 25 cm = 0.25 m; h =6 m

Volume of the cuboid = l×b×h

=(24×0.25×6) m3=36 m3

Total Surface area = 2(lb + lh+ bh)

=2(24×0.25 +24×6 +0.25×6) m2=2(6+144 + 1.5) m2=2×151.5 m2=303 m2

Lateral surface area = 2(l+b)×h

=[2(24+0.25)×6] m2=[2×24.25×6] m2=291 m2

Step-by-step explanation:

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Answer 2

Answer: Height = 11cm