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 t0, the base's side is 4 kilometers and the height is 9 kilometers. What is the rate of change of the surface areaS(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)
Q. 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 t0, 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)
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), where b(t) is the length of the side of the base and h(t) is the height of the prism.
Choose Correct Equation: Choose the correct equation that represents the surface area of a square prism.From the options given, the correct formula that represents the surface area of a square prism is:(C) S(t)=2[b(t)]2+4b(t)h(t)This is because the surface area of a square prism is the sum of the area of the two square bases (2[b(t)]2) and the area of the four rectangular sides (4b(t)h(t)).
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