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There is 1,000 cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. is this enough aluminum for a trophy that has a base edge of 10 cm and a slant height of 13 cm?

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taskmasters
Calculation of the volume of the pyramid will require us to use the equation,
                                       V = Bh/3
where B is the area of the base and h is the height (right). 
 Assuming that the base is a square such that its area is equal to the square of the base edge measurement.
                             B = (10 cm)² = 100 cm²
Given that the base edge is 10 and the slant height is 13, the vertical height is equal to 12 cm. 

The volume is therefore,
                                   V = (100 cm²)(12 cm) / 3 = 400 cm³
Therefore, the aluminum available is still enough. 
Lanuel

Yes, the available aluminum is enough to cast for a trophy because it is less than 1,000 [tex]cm^3[/tex].

Given the following data:

  • Volume of aluminum = 1,000 [tex]cm^3[/tex].
  • Base edge = 10 cm.
  • Slant height = 13 cm.

To determine if the available aluminum is enough to cast for a trophy:

How to calculate the volume of a pyramid.

Mathematically, the volume of a pyramid is given by the formula:

[tex]Volume = \frac{1}{3} \times base \;area \times height[/tex]

For the base area:

[tex]Base\;area = s^2\\\\Base\;area = 10^2[/tex]

Base area = 100 [tex]cm^2[/tex]

For the height:

Height = 12 cm.

Now, we can calculate its volume:

[tex]Volume = \frac{1}{3} \times 100 \times 12\\\\Volume = \frac{1}{3} \times 1200[/tex]

Volume = 400 [tex]cm^3[/tex].

Therefore, the available aluminum is enough to cast for a trophy because it is less than 1,000 [tex]cm^3[/tex].

Read more on volume of a pyramid here: https://brainly.com/question/16315790

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