Question

There is 1000cm3 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.

Answer 1

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,

                                               $Volume, V = a^{2}\frac{h}{3}$.....................................(1)

                     Where, a - Base edge value

                                  h - Height of pyramid

                      From given,

                                        a = 10 cm

                                        h = 13 cm

                      Equation (1) becomes,

                                           $= 10^{2}(\frac{13}{3} )$

                                           $= (100)(4.333)$

                                           $= 433.33 cm^{3}$

             Volume of trophy = 433.33 cubic centimeters

             Compare with the volume of available aluminium and volume of right square pyramid,                          

            $Volume of available aluminium > Volume of right square pyramid$

                                               $1000 cm^{3} > 433.33 cm^{3}$

            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.

Answer 2

Answer:

Yes, the volume of the trophy is 400 cm3