Answer:
The corresponding increase in surface area of the rectangular prism for an increase of 0.9 cm in height is given by
ΔS = [1.8 (L + B)] cm
where L = length of the rectangular prism
B = Breadth of the rectangular prism
Step-by-step explanation:
A rectangular prism is essentially a cuboid.
The surface area of the cuboid is given as
S = 2[LB + LH + BH]
where
L = length of the rectangular prism
B = Breadth of the rectangular prism
H = Height of the rectangular prism
S = 2LB + 2LH + 2BH
Derivative explains that, for small changes in the two quantities,
(∂S/∂H) = (ΔS/ΔH)
ΔS = ΔH × (∂S/∂H)
S = 2LB + 2LH + 2BH
(∂S/∂H) = 2L + 2B = 2(L + B)
ΔH = 0.9 cm
ΔS = ΔH × (∂S/∂H)
ΔS = 0.9 × 2(L + B) = 1.8 (L + B)
A rectangular prism is essentially a cuboid.
The surface area of the cuboid is given as
S = 2[LB + LH + BH]
where
L = length of the rectangular prism
B = Breadth of the rectangular prism
H = Height of the rectangular prism
S = 2LB + 2LH + 2BH
If the height of the rectangular prism increases by 0.9 cm
S(new) = (2×L×B) + 2L(H + 0.9) + 2B(H + 0.9)
S(new) = 2LB + 2LH + 1.8L + 2BH + 1.8B
S(new) = 2LB + 2LH + 2BH + 1.8L + 1.8B
The old surface area, S = 2LB + 2LH + 2BH
Hence, the change or increase in surface area is S(new) - S
[2LB + 2LH + 2BH + 1.8L + 1.8B] - [2LB + 2LH + 2BH] = 1.8L + 1.8B = 1.8 (L + B)
Still the same increase in surface area as obtained by the first method.
Hope this Helps!!!
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