Respuesta :
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,
[tex]Volume, V = a^{2}\frac{h}{3}[/tex].....................................(1)
Where, a - Base edge value
h - Height of pyramid
From given,
a = 10 cm
h = 13 cm
Equation (1) becomes,
[tex]= 10^{2}(\frac{13}{3} )[/tex]
[tex]= (100)(4.333)[/tex]
[tex]= 433.33 cm^{3}[/tex]
Volume of trophy = 433.33 cubic centimeters
Compare with the volume of available aluminium and volume of right square pyramid,
[tex]Volume of available aluminium > Volume of right square pyramid[/tex]
[tex]1000 cm^{3} > 433.33 cm^{3}[/tex]
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.
