Math

1.Which solid has one base that is a triangle and three lateral surfaces that are triangles?

A:Triangular Pyramid***
B:Triangular Prism
C:Rectangular Prism
D:Rectangular Pyramid

2.A solid with two parallel and congruent bases cannot be which of the following:
A:Cone***
B:Prism
C:Cylinder
D:Cube

3.A cone has a radius of 15 cm and a volume of 540 cm^3. Find the volume of a similar cone with a radius of 10 cm.

A:54 cm^3
B:240 cm^3
C:160 cm^3
D:360 cm^3
How do I solve 3?

asked by Reeces
  1. #1 #2 are ok

    the volumes are in the cube of the linear ratio. So, v' = (10/15)^3 v = 8/27 v = 160

    This is due to the fact that each dimension scales the same way. In the case of the sphere, replace r by (2/3)r in the formula. Then you get

    v = 4π/3 r^3
    v' = 4π/3 (2/3 r)^3
    = 4π/3 (2/3)^3 r^3
    = (2/3)^3 v

    posted by Steve
  2. Thanks!

    posted by Reeces
  3. Are you sure number 2 is good, i thought it was sphere

    posted by secret

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