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2 years ago

A cone is 10 inches tall and has a radius of 3 inches. What is the cone's volume?

Mathematics

1 answer:

Mandarinka [93]2 years ago

7 0

The Answer is 94.2 cubic inches

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Where are three places you might find line segments in the real world?

egoroff_w [7]

Answer:

<u><em>Real-world examples of line segments are a pencil, a baseball bat, the cord to your cell phone charger, the edge of a table, etc. Think of a real-life quadrilateral, like a chessboard; it is made of four line segments</em></u>

Step-by-step explanation:

Hope this helps:)

5 0

3 years ago

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y=√x and y=x^2. Find V either by sl

Ede4ka [16]

Answer:

The volume of the solid is $3\pi/10$

Step-by-step explanation:

In this case, the washer method seems to be easier and thus, it is the one I will use.

Since the rotation is around the y-axis we need to change de dependency of our variables to have $f(x)\rightarrow f(y)$ . Thus, our functions with $y$ as independent variable are:

$x=\sqrt{y}\\ x=y^2$

For the washer method, we need to find the area function, which is given by:

$A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]$

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function $x=\sqrt{y}$ and the inner one by $x=y^2$ . Thus, the area function is:

$A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)$

Now we just need to integrate. The integration limits are easy to find by just solving the equation $\sqrt(y)=y^2$ , which has two solutions $y=0$ and $y=1$ . These are then, our integration limits.

$V=\pi\int_{0}^1 (y-y^4)dy\\ V=\pi (\int_{0}^1 ydy - \int_{0}^1 y^4dy)\\ V=\pi/2-\pi/5\\\boxed{V=3\pi/10}$

3 0

3 years ago

Please help me im very behind

Crazy boy [7]

Answer:

the third one should be it

6 0

3 years ago

TIMED!!!

guajiro [1.7K]

Answer: Last option.

Step-by-step explanation:

The total amount of concrete in the ramp ( $V_t$ ) will be the sum of the volume of the rectangular prism ( $V_{rp}$ ) and the volume of the triangular prism ( $V_{tp}$ )