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3 years ago

What is the height of a cone with a radius of 2 inches and volume of 6 cubic inches? Round your answer to the tenths place.

Mathematics

2 answers:

MissTica3 years ago

7 0

I hope this helps you

wlad13 [49]3 years ago

3 0

Answer: 1.4 inches

Step-by-step explanation:

The volume of cone is given by :-

$V=\dfrac{1}{3}\pi r^2 h$ , where r is radius and h is height of the cone.

Given: Volume of cone = 6 cubic inches

Radius =2 inches

Let h be the height of the cone .

Then , the volume of the cone will be :-

$6=\dfrac{1}{3}(3.14) (2)^2(h)\\\\\Rightarrow\ h=\dfrac{6\times3}{(3.14)(2)^2}=1.433121019\approx1.4$

Hence, the height of the cone = 1.4 inches

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What is the area of a circle whose equation is (x-3)² + (y + 1) ² =81?

kupik [55]

Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle:

$\frac{(x-x_{1})^2}{r^2}+ \frac{(y-y_{1})_^2}{r^2}=1$

Where $(x_{1}, y_{1})$ is the centre of the circle. In this case, we don't need to know the centre. Just the radius.

Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81.

$\frac{(x-3)^2}{81}+ \frac{(y+1)^2}{81}=1$

Great! We now know the radius of the circle. It is $\sqrt{81}$ because it is the bottom fraction. Now we know that the radius is 9.

So now lets input this into the area of circle formula:

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Now we insert our radius.

$A=9^2π$

$=A=81π$

You can convert that into a decimal if you wish.

Hope this helped!

~Cam943, Moderator

4 0

3 years ago

The radius r of a cone is increasing at a rate of 4in/min. The height h of the cone is always 4 times the radius. Find the rate

AlekseyPX

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\qquad h=4r\implies V=\cfrac{\pi r^2 \cdot 4r}{3}\implies V=\cfrac{4\pi r^3}{3}\\\\
-----------------------------\\\\
\cfrac{dv}{dt}=\cfrac{4\pi }{3}\cdot 3r^2\cdot \cfrac{dr}{dt}\implies \cfrac{dv}{dt}=4\pi r^2\cdot \cfrac{dr}{dt}\qquad 
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3 years ago

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Fed [463]

Answer:

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Step-by-step explanation:

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2 years ago

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Which solid has a greater volume?

vivado [14]

Answer:

Step-by-step explanation:

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3 years ago

-8x+2y=-2 4x+4y=-4 What is the solution to the system

pickupchik [31]

The solution to system is x = 0 and y = -1

Solution:

Given system of equations are:

-8x + 2y = -2 ----------- eqn 1

4x + 4y = -4 ---------- eqn 2

We have to solve the system of equations

We can solve the equations by elimination method

Multiply eqn 2 by 2

8x + 8y = -8 ------ eqn 3

Add eqn 1 and eqn 3

-8x + 2y = -2

8x + 8y = -8

( + ) ---------------

0x + 2y + 8y = -2 - 8

10y = -10

Divide both sides by 10

y = -1

Substitute y = -1 in eqn 1

-8x + 2(-1) = -2

-8x - 2 = -2

-8x = -2 + 2

x = 0

Thus the solution to system is x = 0 and y = -1

3 0

3 years ago