Question

25 IF YOU ANSWER ALL QUESTIONS!!

Part B Draw the net of the solid that best models the hay bales. Please include the correct dimensions on your net.

Part C
Write a polynomial function S(x), to represent the surface area of the round bale with the givin dementions.

Part D
Using your function from part C, how many square feet of plastic will leonoras family need to wrap a hay bale when x=2.5feet?
Type the correct answer in the box. represent your answer in terms of TT and do not round
(___) TT square feet
Part E
write a polynomial function V to represent the volume of a round bale with the givin dimensions.
V(x)=
Part F
Using your function from part E, how much does a hay bale weigh when x=2.5 feet? Consider that a hay bale weighs approximately 11 pounds per cubic foot and that there are 2,000 pounds in 1 ton.
1. The volume of a hay bale when x=2.5 feet is (____) TT cubic feet.
2. The weight of that hay bale is approximately (____), which is about (____)​

Answer 1

The net of the solid with dimensions 2x and x + 1.5 consists of two rectangles. The surface area polynomial function is S(x) = 12x^2 + 14x, with S(2.5) = 110 square units. The volume polynomial function is V(x) = 2x^3 + 6x^2 + 4.5x. When x = 2.5, the hay bale weighs 880 pounds based on the volume and given weight density.

Part B: Drawing the Net of the Solid

The net of the solid, with length 2x and width x + 1.5, consists of two rectangles. The dimensions of each rectangle are 2x by x + 1.5.

Part C: Surface Area Polynomial Function S(x)

Surface area S(x) of the rectangular solid is given by the formula: S(x) = 2lw + 2lh + 2wh. Substituting the given dimensions, S(x) = 2(2x)(x + 1.5) + 2(2x)(2x) + 2(x + 1.5)(2x), which simplifies to 12x^2 + 14x.

Part D: Surface Area Calculation

Substitute x = 2.5 into S(x): S(2.5) = 12(2.5)^2 + 14(2.5) = 110.

Part E: Volume Polynomial Function V(x)

Volume V(x) of the rectangular solid is given by the formula: V(x) = lwh. Substituting the given dimensions, V(x) = 2x(x + 1.5)(x + 1.5), which simplifies to 2x^3 + 6x^2 + 4.5x.

Part F: Weight Calculation

To find the weight when x = 2.5, use the volume V(2.5) in conjunction with the given weight density: Weight = V(2.5) * Weight Density. Substitute x = 2.5 into V(x): V(2.5) = 2(2.5)^3 + 6(2.5)^2 + 4.5(2.5) = 80. Now, calculate the weight: Weight = 80 * 11 = 880.