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2 years ago

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).

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jok3333 [9.3K]

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kondaur [170]

Answer:

The equation of the line is:

$y=(-\frac{1}{2})x+1$

Therefore, option a is the correct answer.

Step-by-step explanation:

Given the points

(-2, 2)

(4, -1)

Finding the slope

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)$

$m=\frac{-1-2}{4-\left(-2\right)}$

$m=-\frac{1}{2}$

As the point-slope form of the equation of the line is

$y-y_1=m\left(x-x_1\right)$

where m is the slope

substituting the values $m=-\frac{1}{2}$ and the point (-2, 2)

$y-y_1=m\left(x-x_1\right)$

$y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)$

$y-2=\frac{-1}{2}\left(x+2\right)$

$y-2=-\frac{1}{2}\left(x+2\right)$ ∵ $\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

Add 2 to both sides

$y-2+2=-\frac{1}{2}\left(x+2\right)+2$

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Hence, the equation of the line is:

$y=(-\frac{1}{2})x+1$

Therefore, option a is the correct answer.

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tiny-mole [99]

Answer:

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Step-by-step explanation:

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