Acandle 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?

To create one set of candles is needed  or   of wax

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

step 1

Find the volume of the smallest candle

we have

substitute

step 2

Find the volume of the second candle

Remember that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

we have

the scale factor is equal to

The volume of the second candle is equal to

step 3

Find the volume of the third candle

Remember that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

we have

the scale factor is equal to

The volume of the third candle is equal to

step 4

To find the total wax needed, sum the volume of the three candles

so

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)