Question

A pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism. So its volume is _____times the volume of the smaller prism.
A) 64
B) 8
C)16
D)4

Would it be A) 64?

Next Question: If the dimensions of a cylinder are doubled the surface area will be _______? Would it be doubled?

Thank you for the help

Answer 1

Volumes are (linear ratio)³ and
areas are (linear ratio)²

Answer 2

1. V = 2.83*r^2*h.
V1/V2 = 2.83*(4r)^2*4h/(2.83*r^2*h)
V1/V2 = 16r^2*4h/(r^2*h = 64.

2. A1 = 2pi*r^2 + 2pi*r*h
A1 = 2pi*r(r+h)

A2/A1 = (2pi*2r(2r+2h))/(2pi*r(r+h)
A2/A1 = (4pi*r(2r+2h))/(2pi*r(r+h)
A2/A1 = 2(2(r+h)/(r+h) = 4.

2. A shorter Method
A1 = 2pi*r(r+h). Let r = 1, and h = 2.
A1 = 6.28*1(1+2) = 18.84 Sq. Units.

Double r, and h.
A2 = 6.28*2(2+4) = 75.36 Sq. Units.

A2/A1 = 75.36/18.84 = 4.

Answer 3

64, Quadrupled