By what number do you need to multiply the volume of the cone to get the volume of the cylinder?

1 answer:

8 0

You need to multiply the volume of a cone by 3 to get the volume of its corresponding cylinder (a cylinder with the same base radius and perpendicular height).

As in:

Vol. of a cylinder= πr²h

and Vol. of a cone= ⅓πr²h

So assuming volume of a cone is ⅓V, then the volume of the cylinder will be ⅓V × 3 which equals V.

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Identify the diameter of the circular base created by folding the figure into a right cone. HELP ASAP PLEASE!!

Akimi4 [234]

let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.

think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.

now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area. Well, what is the circumference of that shaded area?

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies C=2\pi 12\implies C=24\pi \implies \stackrel{\textit{three quarters of it}}{24\pi \cdot \cfrac{3}{4}} \\\\\\ 6\pi \cdot 3\implies 18\pi$

well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=18\pi \end{cases}\implies 18\pi =2\pi r\implies \cfrac{18\pi }{2\pi }=r\implies 9=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{diameter is twice the radius}}{d=18}~\hfill$

3 0

3 years ago

Pls answer this with a picture showing the correct box plot

faust18 [17]

Answer/Step-by-step explanation:

To find out the mistake of the student, let's find the min, max, median, Q1 and Q3, which make up the 5 important values that are represented in a box plot.

Given, {2, 3, 5, 6, 10, 14, 15},

Minimum value = 2

Median = middle data point = 6

Q1 = 3 (the middle value of the lower part of the data set before the median)

Q3 = 14 (middle value of the upper part of the data set after the median)

Maximum value = 15

If we examine the diagram the student created, you will observe that he plotted the median wrongly. The median, which is represented by the vertical line that divides the box, ought to be at 6 NOT 10.

See the attachment below for the correct box plot.