Question

Example 4: An aquarium is in the form of a cuboid whose external measures are
80 cm x 30 cm x 40 cm. The base, side faces and back face are to be covered with a
coloured paper. Find the area of the paper needed?​

Answer 1

Answer:

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\linethickness{.4mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{80 cm}}\put(3.8,6.3){\sf{30 cm}}\put(11.2,7.5){\sf{40 cm}}\end{picture}$

• Length ( L )= 80 cm
• Breadth ( B ) = 30 cm
• Height ( H ) = 40 cm

As all faces of cuboid are in the shape of rectangle, hence we can find its area by the formula (Length × Breath)

⠀

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Area=Base+Side\:Faces+Back\:Face\\\\\\:\implies\sf Area=(LB)+[(BH)+(BH)]+(LH)\\\\\\:\implies\sf Area=(LB)+2(BH)+(LH)\\\\\\:\implies\sf Area=(80 \times 30)+2(30 \times 40)+(80 \times 40)\\\\\\:\implies\sf Area = 2400 + (2 \times 1200) +3200\\\\\\:\implies\sf Area = 2400 + 2400 + 3200\\\\\\:\implies\sf Area = 8000 \:cm^{2}\\\\\\:\implies\sf Area =8000 \times \dfrac{1}{100} \:m \times \dfrac{1}{100} \:m\\\\\\:\implies\sf Area = 0.8 \:m^{2}$

⠀

$\therefore\:\underline{\textsf{Hence, Area of paper needed is \textbf{0.8 m ^\text2 }}}.$

Answer 2

Appropriate Question :-

• An aquarium is in the form of a cuboid whose external measures are 80 cm x 30 cm x 40 cm. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?

Required Answer :-

• Area of the paper required =7000 cm²

Dimensions of an Aquarium :-

• Length (l) = 80 cm,

• Breadth (b) = 30 cm,

• Height (h) = 40 cm

According to the problem given,

• Area of the paper required = Area of the base + 2×Area of two side faces + Area of the back side

(Front side should be visible,So, it is not covered )

• => lb+2×bh+lh

• => 80×30+2×(30×40)+80×40

• => 2400+2×1200+3200

• => 2400+2400+3200

• => 7000 cm²

Therefore,

• Area of the paper required =7000 cm

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Note :-

• Diagram is in attachment. kindly go through it for better understanding ! :D