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? a) 27π cubic inches b) 36π cubic inches c) 53π cubic inches d) 86π cubic inchese) 98π cubic inches

63.565 inch³

Step-by-step explanation:

A candle manufacturer sells cylindrical candles in sets of three.

Each candle in the set is of different size.

Smallest candle has a radius of [tex]r_{1}[/tex] = 0.5 inches and a height of [tex]h_{1}[/tex] = 3 inches.

other two candles are with scale factors of 2 and 3.

It means radius and height for second candle are [tex]r_{2}[/tex] = 0.5 × 2 = 1 inch and [tex]h_{2}[/tex] = 3 × 2 = 6 inches.

Radius and height of third candle are [tex]r_{3}[/tex] = 0.5 × 3 = 1.5 inch and [tex]h_{3}[/tex] = 2 × 3 = 6 inches

Now we have to calculate the amount of wax needed to create one set of candles.

Volume of Candle 1 = [tex]\pi r_{1}^{2}h_{1}[/tex]

= [tex]\pi (0.5)^{2}(3) = 3.14(0.25)(3)=2.355inches^{3}[/tex]

Volume of Candle 2 = [tex]\pi r_{2}^{2}h_{2}^[2][/tex]

= [tex]\pi (1)^{2} (6)=(3.14(6)=18.84inch^{3}[/tex]

Volume of Candle 3 = [tex]\pi r_{3}^{2}h_{3}^[2][/tex]

= [tex](3.14)(1.5)^{2}(6)=42.39inch^{3}[/tex]

Total quantity of wax = Volume (1) + volume (2) + volume (3)

= 2.355 + 18.84 + 42.39 = 63.565 inch³

63.565 inch³ wax is needed to create one set of candles.

A is the answer for your question

86 cubic inches

Step-by-step explanation:

It is possible to suppose that the candles have a perfect cylindrical form.

The volume of a cylinder with radius r and height h is:

Knowing the dimensions of each candle it is possible to calculate the total volume required. Due to the scale data, the dimensions of each candle is:

C1: (r=0.5 inches, h=3 inches)

C1: (r=1 inches, h=6 inches)

C1: (r=1.5 inches, h=9 inches)

So, the total volume may be calculated as:

Vt≈86 cubic inches

So, the smallest candle has a radius r = 0.5 and a height of h = 3.

now, the other two candles in the set, are scaled of 2(twice as large) and of 3(thrice as large).

therefore, the candle scaled at 2 has a radius of 2*0.5 or 1, and a height of 2*3 or 6.

and the last candle in the set scaled t 3 has a radius of 3*0.5 or 1.5, and a height of 3*3, or 9

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\\\\ -------------------------------\\\\ \stackrel{r=0.5~~h=3}{\pi \cdot 0.5^2\cdot 3}~~~+~~~\stackrel{r=1~~h=6}{\pi \cdot 1^2\cdot 6}~~~+~~~\stackrel{r=1.5~~h=9}{\pi \cdot 1.5^2\cdot 9} \\\\\\ 0.75\pi ~~~+~~~6\pi ~~~+~~~20.25\pi \implies 27\pi[/tex]

Amount of wax required = 508.93 cubic inches

Step-by-step explanation:

Volume = Base area x Height.

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

Radius of other candles = 0.5 x 2 and 0.5 x 3

= 1 inch and 1.5 inch

Height of other candles = 3 x 2 and 3 x 3

= 6 inch and 9 inch

Base area of cylinder

[tex]A = \pi \: {r}^{2}[/tex]

Volume of candles

[tex]V=\pi r_1^2h_1+\pi r_2^2h_2+\pi r_3^2h_3\\\\V=\pi \times 0.5^2\times 3+\pi \times 1^2\times 6+\pi \times 1.5^2\times 9=503.98inch^3 \\[/tex]

Amount of wax required = 508.93 cubic inches

A is the answer let me know if that was right

Step-by-step explanation:

8.5inches of wax is needed to make the candles.

: )

27 pi in³

Step-by-step explanation:

I just took a test on Plato/Edmentum with this question and this was the right answer

~Please mark me as brainliest 🙂

b

Step-by-step explanation:

dont trust me could be wrong

A. 27 π cubic inches

Step-by-step explanation:

The volume of a cylinder is calculated using the formula;

[tex]Volume=\pi r^2h[/tex]

From the given information, the smallest candle has a radius of 0.5 inches and a height of 3 inches.

We substitute [tex]r=0.5[/tex] and [tex]h=3[/tex] into the given formula.

The vlume of the smallest candle is

[tex]Volume=\pi \times0.5^2\times 3[/tex]

[tex]Volume=\frac{3}{4}\pi in^3[/tex]

from the given information, the other two candles are scaled versions of the smallest, with scale factors of 2 and 3.

The volume of the other two candles will be [tex]2^3\times \frac{3}{4}\pi=6\pi in^3[/tex] and [tex]3^3\times \frac{3}{4}\pi=\frac{81}{4}\pi in^3[/tex]

The wax needed to create one set of candle is

[tex]\frac{3}{4}\pi+6\pi+\frac{81}{4}\pi=27\pi\: in^3[/tex]

The correct answer is A