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Question

Describe the effect of each change of Linear Dimensions on the Volume:

1. The dimensions of a cylinder are tripled.

1. The dimensions of a cone are multiplied by 1/3.

1. The dimensions of a sphere are doubled.

Answer 1

1) use the formula for the volume of a cylinder: V = pi*r²h and assess the impact of tripling your dimensions:

1. V = pi*(3r)²(3h) = pi*9*r²*3*h = 27*pi*r²*h --> your volume is multiplied by a factor of 27

2) use the formula for the volume of a cone: V = pi*r³*h/3 and assess the impact of multiplying your dimensions by 1/3

1. V = pi*(r/3)³*(h/3)/3 = pi*r³*(h/3)*(1/81) --> the volume decreases by a factor of 1/81

3) use the formula for the volume of a sphere: V = 4/3*pi*r³ and assess the impact of doubling your radius

1. V = 4/3*pi*(2*r)³ =4/3*pi*r³*8 --> the volume increases by a factor of 8