The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.
Step-by-step explanation:
The given is,
Volume of aluminium available is 1000 cubic centimeters
Shape of trophy is right square pyramid
Trophy has a base edge of 10 cm and slant height of 13 cm
Step:1
Formula for volume of right square pyramid,
.....................................(1)
Where, a - Base edge value
h - Height of pyramid
From given,
a = 10 cm
h = 13 cm
Equation (1) becomes,
![= (100)(4.333)](https://tex.z-dn.net/?f=%3D%20%28100%29%284.333%29)
![= 433.33 cm^{3}](https://tex.z-dn.net/?f=%3D%20433.33%20cm%5E%7B3%7D)
Volume of trophy = 433.33 cubic centimeters
Compare with the volume of available aluminium and volume of right square pyramid,
![Volume of available aluminium > Volume of right square pyramid](https://tex.z-dn.net/?f=Volume%20of%20available%20aluminium%20%3E%20Volume%20of%20right%20square%20pyramid)
![1000 cm^{3} > 433.33 cm^{3}](https://tex.z-dn.net/?f=1000%20cm%5E%7B3%7D%20%3E%20433.33%20cm%5E%7B3%7D)
So, the given volume of aluminium is enough to make right square pyramid shaped trophy.
Result:
The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.