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Urpi was given this problem:
The side 
b(t) of the base of a square prism is decreasing at a rate of 7 kilometers per minute and the height 
h(t) of the prism is increasing at a rate of 10 kilometers per minute. At a certain instant 
t_(0), the base's side is 4 kilometers and the height is 9 kilometers. What is the rate of change of the surface area 
S(t) of the prism at that instant?
Which equation should Urpi use to solve the problem?
Choose 1 answer:
(A) 
S(t)=6[b(t)]^(2)
(B) 
S(t)=[b(t)]^(3)
(C) 
S(t)=2[b(t)]^(2)+4b(t)*h(t)
(D) 
S(t)=[b(t)]^(2)*h(t)

Urpi was given this problem:\newlineThe side b(t) b(t) of the base of a square prism is decreasing at a rate of 77 kilometers per minute and the height h(t) h(t) of the prism is increasing at a rate of 1010 kilometers per minute. At a certain instant t0 t_{0} , the base's side is 44 kilometers and the height is 99 kilometers. What is the rate of change of the surface area S(t) S(t) of the prism at that instant?\newlineWhich equation should Urpi use to solve the problem?\newlineChoose 11 answer:\newline(A) S(t)=6[b(t)]2 S(t)=6[b(t)]^{2} \newline(B) S(t)=[b(t)]3 S(t)=[b(t)]^{3} \newline(C) S(t)=2[b(t)]2+4b(t)h(t) S(t)=2[b(t)]^{2}+4 b(t) \cdot h(t) \newline(D) S(t)=[b(t)]2h(t) S(t)=[b(t)]^{2} \cdot h(t)

Full solution

Q. Urpi was given this problem:\newlineThe side b(t) b(t) of the base of a square prism is decreasing at a rate of 77 kilometers per minute and the height h(t) h(t) of the prism is increasing at a rate of 1010 kilometers per minute. At a certain instant t0 t_{0} , the base's side is 44 kilometers and the height is 99 kilometers. What is the rate of change of the surface area S(t) S(t) of the prism at that instant?\newlineWhich equation should Urpi use to solve the problem?\newlineChoose 11 answer:\newline(A) S(t)=6[b(t)]2 S(t)=6[b(t)]^{2} \newline(B) S(t)=[b(t)]3 S(t)=[b(t)]^{3} \newline(C) S(t)=2[b(t)]2+4b(t)h(t) S(t)=2[b(t)]^{2}+4 b(t) \cdot h(t) \newline(D) S(t)=[b(t)]2h(t) S(t)=[b(t)]^{2} \cdot h(t)
  1. Understand Problem and Formula: Understand the problem and determine the formula for the surface area of a square prism. A square prism's surface area is composed of the areas of the three pairs of parallel faces: the two square bases and the four rectangular sides. The formula for the surface area of a square prism is S(t)=2[b(t)]2+4b(t)h(t)S(t) = 2[b(t)]^2 + 4b(t)h(t), where b(t)b(t) is the length of the side of the base and h(t)h(t) is the height of the prism.
  2. Choose Correct Equation: Choose the correct equation that represents the surface area of a square prism.\newlineFrom the options given, the correct formula that represents the surface area of a square prism is:\newline(C) S(t)=2[b(t)]2+4b(t)h(t)S(t) = 2[b(t)]^2 + 4b(t)h(t)\newlineThis is because the surface area of a square prism is the sum of the area of the two square bases (2[b(t)]22[b(t)]^2) and the area of the four rectangular sides (4b(t)h(t)4b(t)h(t)).

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