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Nitella [24]
3 years ago
12

A box has the shape of a rectangular prism with height 30 cm. If the height is increased by 0.9 ​cm, by how much does the surfac

e area of the box​ increase?
Use pencil and paper. Show your work. Then show a second way to solve the problem. Explain which way you like better and why.
Mathematics
1 answer:
crimeas [40]3 years ago
4 0

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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Question 1
Ahat [919]

Answer: x = 22


Explanation:


1) Corresponding sides and correspoding angles of congruent triangles are equal.


2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.


That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:


  • ∠A and ∠D are congruent
  • ∠B and ∠ E are congruent
  • ∠C and ∠F are congruent
  • Segment AB and segment DE are congruent
  • Segment BC and segment EF are congruent
  • Segment AC and segment  DF are congruent

In the figures, it is given that the segment DF measures (1/2)x  - 1 and the corresponding segment AC measures 10 units.


Hence, you set this equation: (1/2)x - 1 = 10


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