Plato Question for Extending three dimensions

Question

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles?

A. 

27  cubic inches

B. 

36  cubic inches

C. 

53  cubic inches

D. 

86  cubic inches

E. 

98  cubic inches

Answer 1

V_small = π(0.5)²(3)

V_midium = 8 V_small

V_large = 27 V_small

Answer 2

Hi,

In fact, you need to find volume of 3 candles with different size,

smallest candle: r = 0.5 h = 3 V₁ = pi r^2 h = ( .5)^2 (3)pi = 0.75pi

r = 1 h = 6 V_{2 =} pi r^2 h =( 1)^2 (6)pi = 6pi

r= 1.5 h = 9 V₃ =pi r^2 h = ( 1.5)^2 (9 )pi = 20.25pi

set of candles needs to V₁ + V₂ +V₃= (0.75 + 6+ 20.25) pi = 27pi cube inches

I hope it is useful,

Minoo