A sporting goods company sells a tent with the dimensions shown. The company wants to introduce a new, larger tent that is geometrically similar to the original tent but with a height of 6 feet. How will the volume of the new tent compare with the volume of the original tent?

The volume of the new tent will be 3/2 times the volume of the original

Step-by-step explanation:

The original tent is a triangular prism, which missing dimensions of the tent are:

base (b) : 6 ft height (h) : 4 ft length (l) : 7 ft

Volume of the original tent:

V = 1/2*b*h*l

The only difference between the new and the original tent are their heights. Let's call h' = 6 ft to the height of the new tent.

Volume of the new tent:

V' = 1/2*b*h'*l

Dividing V' by V:

V'/V = (1/2*b*h'*l) / (1/2*b*h*l)

V'/V = h'/h

Replacing with dа ta:

V'/V = 6/4

V' = 3/2*V