SERIOUSLY NEED HELP WITH THIS QUESTION.
2 answers:
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that the volume of cube is 1,000 cubic feet.
The volume of cube is
The side length of cube is 10 feet.
It is given that the other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height.
The area of tilted solid is
Since height and base are same, so the area of tilted solid is
The volume of the tilted solid is 1,000 cubic feet. Therefore the correct option is 2.
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If you look at the pyramid, the pyramid is really just a hexagon with 6 triangles stacked up to each other at the edges, with the hexagon at the bottom.
now, the perpendicular distance from the center of the hexagon to a side, namely the apothem, is 6√3, and each side is 12 units long, since there are 6 of them that'd be 72 for all, namely the perimeter.
each of the triangular faces have a base of 12 and an altitude or height of 11, recall that area of a triangle is (1/2)bh, and area of a regular polygon is (1/2)(apothem)(perimeter).
so if we just get the area of the hexagon at the bottom, and the triangles, sum them up, that's the surface area of the pyramid.
![\bf \stackrel{\textit{area of the hexagon}}{\left[\cfrac{1}{2}(6\sqrt{3})(72) \right]}~~~~+~~~~\stackrel{\textit{area of the 6 triangles}}{6\left[\cfrac{1}{2}(12)(11) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20hexagon%7D%7D%7B%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%286%5Csqrt%7B3%7D%29%2872%29%20%20%5Cright%5D%7D~~~~%2B~~~~%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%206%20triangles%7D%7D%7B6%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%2812%29%2811%29%20%20%5Cright%5D%7D)
now, the perpendicular distance from the center of the hexagon to a side, namely the apothem, is 6√3, and each side is 12 units long, since there are 6 of them that'd be 72 for all, namely the perimeter.
each of the triangular faces have a base of 12 and an altitude or height of 11, recall that area of a triangle is (1/2)bh, and area of a regular polygon is (1/2)(apothem)(perimeter).
so if we just get the area of the hexagon at the bottom, and the triangles, sum them up, that's the surface area of the pyramid.