1. Find the volume, lateral surface area and the total surface area of the cuboid whose
dimensions are:
(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm
(ii) length = 15 m, breadth = 6 m and height = 9 dm
(iii) length = 24 m, breadth = 25 cm and height = 6 m
(iv) length = 48 cm, breadth = 6 dm and height = 1 m
Answers
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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