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Q.

A rectangular box has a uniform cross-section with length,breadth and height are 4, 5 and 4 cm, then calculate the volume and surface area of the box.

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a

Volume=144

c m^{3}

, area =40

c m^{2}

b

Volume=80

c m^{3}

, area =144 c

m^{2}

c

Volume=144

c m^{3}

, area =80 c

m^{2}

d

Volume=24

c m^{3}

, area =414 c

m^{2}

answer is B.

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Detailed Solution

Concept: Volume simply means how much space that 3D body can occupy . Surface area means how much area its faces have ,it can be lateral and total surface area. Following are the various formulae surface area and volume of several 3D objects
Cuboid total surface area=2(lb+bh+lh), lateral surface Area=2h(l+b), volume = lbh where l,b and h are the length ,breadth and height of the cuboid.
Cube - Total surface area=6 ×

lengt h^{2}

Lateral surface area = 4 ×

lengt h^{2}

Volume=

length 3

Similarly, we can find surface area and volume of several other shapes.
Given:Various dimensions of cuboid are,
Length

(l) = 4 cm

Breadth

(b) = 5 cm

Height

(h) = 4 cm

Volume

= lbh = 4 \times 5 \times 4 = 80

cubic cm
Lateral surface area

= 2 (l + b) \times h

= 2 (4 + 5) \times 4 = 2 \times 9 \times 8 = 144

square cm
Volume= 80 cubic cm ,Lateral surface area=144 square cm
Hence, option 2) is correct.

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