Respuesta :
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?
in cubic inches
Answer
pi 0.5^2 *3 = 0.75pi is the volume of the first candle.
The second volume is 8 * 0.75pi = 6pi.
And the last volume is 27 * 0.75 pi = 20.25 pi So in total we just take the sum and that is 27pi
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?
in cubic inches
Answer
pi 0.5^2 *3 = 0.75pi is the volume of the first candle.
The second volume is 8 * 0.75pi = 6pi.
And the last volume is 27 * 0.75 pi = 20.25 pi So in total we just take the sum and that is 27pi
Answer:
To create one set of candles is needed [tex]27\pi\ in^{3}[/tex] or [tex]84.82\ in^{3}[/tex] of wax
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
step 1
Find the volume of the smallest candle
we have
[tex]r=0.5\ in[/tex]
[tex]h=3\ in[/tex]
substitute
[tex]V=\pi (0.5^{2})(3)=0.75 \pi\ in^{3}[/tex]
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 [tex]2[/tex]
The volume of the second candle is equal to
[tex]2^{3} *0.75\pi =6\pi\ in^{3}[/tex]
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 [tex]3[/tex]
The volume of the third candle is equal to
[tex]3^{3} *0.75\pi =20.25\pi\ in^{3}[/tex]
step 4
To find the total wax needed, sum the volume of the three candles
so
[tex]0.75\pi\ in^{3}+6\pi\ in^{3}+20.25\pi\ in^{3}=27\pi\ in^{3}[/tex]
[tex]27\pi\ in^{3}=84.82\ in^{3}[/tex]