Question

solve the attachment and don't spam.​

Answer 1

$\large \underline \bold{Given :-}$

$\small \underline \bold{For \: a \: Cubical \: box -}$

$\: \: \: \:$$\small \bold{each \: edge \: (a) = 10 \: cm}$

$\small \underline \bold{For \: another \: Cuboidal \: box -}$

$\: \: \: \:$$\small \bold{length \: (L) = 12.5 \: cm}$

$\: \: \: \:$$\small \bold{width \: (b) = 10 \: cm}$

$\: \: \: \:$$\small \bold{height \: (h) = 8 \: cm}$

$\large \underline \bold{To \: Find :-}$

$\small \bold{Which \: box \: has \: the \: greater \: LSA \: and \: smaller \: TSA \: ?}$

$\large \underline \bold{Usable \: Formulas :-}$

★$\small \underline \bold{For \: a \: Cube -}$

$\small \bold{1) \: Total \: Surface \: Area = 6a^{2}}$

$\small \bold{2) \: Lateral \: Surface \: Area = 4a^{2}}$

★$\small \underline \bold{For \: a \: Cuboid -}$

$\small \bold{1) \: Total \: Surface \: Area = 2(Lb + bh + hL)}$

$\small \bold{2) \: Lateral \: Surface \: Area = 2h(L + b)}$

Firstly ,

$\small \underline \bold{For \: Cubical \: box -}$

$\: \: \: \:$$\small \bold{LSA = 4(10)^{2} = 4(100) = 400 \: cm^{2}}$

$\: \: \: \:$$\small \bold{TSA = 6(10)^{2} = 6(100) = 600 \: cm^{2}}$

Now ,

$\small \underline \bold{For \: Cuboidal \: box -}$

$\small \bold{LSA = 2(8)(12.5 + 10) = 16\times 22.5 = 8(45) = 360 \: cm^{2}}$

$\small \bold{TSA = 2[12.5(10) + 10(8) + 8(12.5)]}$

$\small \bold{TSA = 2[125 + 80 + 100] = 2(305) = 610 \: cm^{2}}$

$\small \bold{On \: Comparing -}$

$\small \bold{(i) \: Cubical \: box \: has \: the \: greater \: lateral \: surface \: area \: by \: 40 \: cm^{2}}$

$\small \bold{(ii) \: Cubical \: box \: has \: the \: smaller \: total \: surface \: area \: by \: 10 \: cm^{2}}$

Answer 2

Answer:

(i) Lateral surface area of cube = 4edge

2

=4(10)

2

=400

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

2×8(12.5+10)

=16×22.5

=360

So, the lateral surface area of the cube is larger by (400−360=40)cm

2

(ii) Total surface area of cube = 6edge

2

=6(10)

2

=600

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

2(12.5×10+10×8+8×12.5)

=2(125+80+100)

=610

So, the total surface area of cuboid is larger by (610−600=10) square cm