Which explanation can be used to informally derive the formula for the volume of a cone?

Mathematics

2 answers:

labwork [276]2 years ago

5 0

Answer: Just took the test and got the answer!! Step-by-step explanation: Look at the image down below ♡＼(￣▽￣)／♡

kvasek [131]2 years ago

4 0

Answer: The answer is (D) A cylinder is exactly 3 times bigger than a cone with the same height and radius. Therefore, the formula for the volume of a cone is 1/3 of the volume of a cylinder with the same height and radius.

Step-by-step explanation: We know that a Cone is a three-dimensional geometric figure with a circular base as shown in the attached figure (a). In fact, a Cone is a pyramid with a circular cross-section.

The volume of a Cone and a Cylinder are related to each other. The volume of a cylinder is

$V_{cylinder}=\pi r^2h$

and the volume of a cone is

$V_{cone}=\dfrac{1}{3}\pi r^2h.$

Therefore, if the radius of the base and height of a cone and a cylinder are same, the the volume of the cone is one-third of the volume of cylinder. So, we can join 3 cones together to form a single cylinder having radius and height equal to the radius of base and height respectively of the cone. See the attached figure (b).

Thus, the correct option is (D).

You might be interested in

line AB passes through points A(-6,6) and B(12,3) if the equation of the line is written in slope intercept form

Paul [167]

Y=(-1/6)x+5
m=(y2-y1)/(x2-x1)
m=(3-6)/(12-(-6))
m=(-3)/(18)
m=-1/6
y=mx+b
y=(-1/6)x+b
6=(-1/6)(-6)+b
6=1+b
b=5
y=(-1/6)x+5

7 0

2 years ago

Write out the following proportions in words. a. 7 :28 = 2 : 8 b. 3⁄1 = 18⁄6 c. 9 : 72 = 2 : 16 d. 81⁄9 = 45⁄5

Lerok [7]

1) Proportion a.

7 : 28 = 2 : 8

That means that the ratio 7 / 28 is equal to the ratio 2 : 8.

You can verify the equality by simplifying to the simplest form:

 7 : 28 = 1 / 4 simplest form
 2 : 8 = 1 / 4 simplest form, then the proportion is right.

In words that is 7 is to 28 as 1 is to 4 ← answer

2) Proportion b.. 3⁄1 = 18⁄6


In words: 3 is to q as 18 is to 6 ← answer


You can verify the proportion by simplifiying the second fraction:


 18 / 6 = [18 / 6] / [ 6 / 6] = 3 / 1


3) Proportion c. 9 : 72 = 2 : 16


In words: 9 is to 72 as 2 is to 16 ← answer


Proove the proportion:


 9 / 72 = 1 / 8


 2 / 16 = 1 / 8


4) Proportion d. 81⁄9 = 45⁄5

In words: 81 is to 9 as 45 is to 5 ← answer

Proove it:
 81 / 9 = 9
 45 / 9 = 9

8 0

2 years ago

Read 2 more answers

Solve. 3 - 2 | 2-5 | + 3

expeople1 [14]

$3-2\left|2-5\left|+3\right\\= -23$