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igor_vitrenko [27]
2 years ago
13

Find the total number of unit cube that fill the entire prism

Mathematics
1 answer:
Nonamiya [84]2 years ago
3 0

Answer:

72 cubes

Step-by-step explanation:

Attached is the picture drawn (though not great one), showing 6 cube on length of prism, 3 cubes on width and 4 cubes on height of prism.

Given: Length of prism= 6

           Width= 3

            Height= 4

To know the number of cubes, which can fill the entire prism, we need to find volume of prism.

∴ Volume of prism= length\times width\times height

Volume of prism= 6\times 3\times 4= 72

∴ 72 units of cube can fill the entire prism.

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1. Carter will install fencing all around the flat area of his
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Answer:

Amount of fencing required = 75 yards

Step-by-step explanation:

Distance between the two points (x_1,y_1) and (x_2,y_2) is given by the formula,

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Distance between A(3, 6) and B(3, -2) = \sqrt{(3-3)^2+(6+2)^2}

                                                               = 8 yards

Distance between B(3, -2) and C(-7, 4) = \sqrt{(3+7)^2+(-2-4)^2}

                                                                = \sqrt{136}

                                                                = 11.66 ≈ 12 yards

Distance between C(-7, 4) and D(-7, -2) = \sqrt{(-7+7)^2+(4+2)^2}

                                                                 = 6 yards

Distance between D(-7, -2) and E(-3, -2) = \sqrt{(-7+3)^2+(-2+2)^2}

                                                                   = 4 yards

Distance between E(-3, -2) and F(-3, -8) = \sqrt{(-3+3)^2+(-2+8)^2}

                                                                = 6 yards

Distance between F(-3, -8) and G(3, -8) = \sqrt{(-3-3)^2+(-8+8)^2}

                                                                 = 6 yards

Distance between G(3, -8) and H(10, -12) = \sqrt{(3-10)^2+(-8+12)^2}

                                                                   = \sqrt{49+16}

                                                                   = \sqrt{65}

                                                                   = 8.06 ≈ 8 yards

Distance between H(10, -12) and J(10, 6) = \sqrt{(10-10)^2+(-12-6)^2}

                                                                   = 18 yards

Distance between A(3, 6) and J(10, 6) = \sqrt{(10-3)^2+(6-6)^2}

                                                               = 7 yards

Since length of fence required = perimeter of the flat area

Perimeter of the given area = 8 + 12 + 6 + 4 + 6 + 6 + 8 + 18 + 7

                                              = 75 yards

Therefore, amount of fencing required = 75 yards

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