All categories

3 years ago

The triangles below are similar. What is the length of ? A. 17 cm C. 19 cm B. 18 cm D. 20 cm

Mathematics

1 answer:

denis-greek [22]3 years ago

4 0

Answer:

B. 18 cm.

Step-by-step explanation:

Because they are similar, we can say that segment AC corresponds to segment DF, and segment AB corresponds to segment ED. So, we can set up a proportion.

$\frac{16}{24} =\frac{12}{x}$

$\frac{2}{3} =\frac{12}{x}$

2 * x = 12 * 3

2x = 36

x = 18

So, the length of ED is B. 18 cm.

Hope this helps!

You might be interested in

Can you teach me how to do, 3ax+2b/c = 4b? Please

Brums [2.3K]

I Also nenes help doing thank

5 0

3 years ago

Read 2 more answers

») What is the volume of a ball with adiameter of 6 centimeters? Use 3.14for (pie)How is the volume of a sphere related tothe vo

Dahasolnce [82]

Volume of a sphere and a cone

We have that the equation of the volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

We have that the radius of a sphere is half the diameter of it:

Then, the radius of this sphere is

r = 6cm/2 = 3cm

<h2>Finding the volume of a sphere</h2>

We replace r by 3 in the equation:

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot3^3 \end{gathered}$

Since 3³ = 3 · 3 · 3 = 27

$\begin{gathered} V=\frac{4}{3}\pi3^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot27 \end{gathered}$

If we use π = 3.14:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot27 \\ \downarrow \\ V=4.18\bar{6}\cdot27 \end{gathered}$

Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:

4.18666... ≅ 4.19

Then, we have that:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=4.19\cdot27 \\ =113.13 \end{gathered}$

Then, we have that:

<h2>Finding the volume of a cone</h2>

We have that the volume of a cone is given by:

$V=\frac{1}{3}\pi r^2h$

where r is the radius of its base and h is the height:

Then, in this case

r = 3

h = 6

and

π = 3.14

Replacing in the equation for the volume:

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \end{gathered}$

Then, we have:

3² = 9

$\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot9\cdot6 \\ V=\frac{1}{3}\cdot3.14\cdot54 \\ V=56.52 \\ \end{gathered}$

Answer: the volume of the cone that has the same circular base and height is 56.52 cm³