What is the maximum volume of a pyramid that can fit inside a cube that has side 18 cm long?

1 answer:

8 0

Formula for Volume of cube= 1/3 x area of base x height
as base and height are the same:
So,
Base = 18 cm
Height = 18 cm
Area of base = Base^2
Area of base = 18^2
Area of base = 324 cm
Putting all the values into the formula:
1/3 x 324 x 18
=6 x 324 
= 1944 cm^3
So according to above explanation
C) 1944 cm3, is the correct answer.

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The area of the following equilateral triangle is 62.4 square feet that is he height

Vikentia [17]

The height of this triangle would be 10.4

In order to find this, you first must find the length of the sides. Using a manipulated formula for area of an equilateral triangle, we can determine the lengths of the side. Below if the formula.

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{A}$

In this, S is the length of the side and A is the area. So we plug in and get:

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{62.4}$

S = $\frac{2}{3}3^{\frac{3}{4}} 7.89$

S = 12

Now that we have the side as 12, we can use the Pythagorean Theorem to find the height. If you split a equilateral triangle down the middle, you are left with two right triangles. Using this right triangle, the hypotenuse would be 12, the first leg would be 6 (half of the base) and the height would be the other leg. So we plug in and solve.

$a^{2} + b^{2} = c^{2}$