find-the-indicated-volumes-by-integration-the-ball-used-in-australian-football-is-elliptical-find--2

Question

Find the indicated volumes by integration.
The ball used in Australian football is elliptical. Find its volume if it is $275 \mathrm{mm}$ long and $170 \mathrm{mm}$ wide.

Stanley Enemuo · Accepted Answer

So the computer analysis in this part tells us surface of the german be approximated luncheon. What? 10 times 1 -1 0.01 Next Square. And that is equal to limits being exceeded 100 and energy. The volume is representing me killed. So why? Oh, function y squared the eggs. You know what? They are definitely answer door. But to do this, we can evaluate this by the substitution and say, let&#x27;s say you was maybe 100 -0.001. We&#x27;re back then. Are you As zero carol one? So as an integral expand. Because it&#x27;s an evil function. We could now take called Many of the answer grow From 0 to 100. And once we take those limits, that&#x27;s when we get uh of volume, which is 68,800.

M S · Answer

so says we have the volume of a sphere is a function of the radius of the spirit, right? A bunch for the volume of a ball and evaluate the function at a radius. Uh, seven point, uh, Centimeters. So we have the equation for the volume. So you and are his radius is what we were playing. It equals 4/3. Hi are cute Nesta function for the volume of a sphere. Now let&#x27;s evaluated when a radius is 10 point loss in commuters. So we just plug in some white boxer or so 4/3 pi times 10 point buck Q. You put this into the calculator, you get 4849 centimeters cube.

Chris Trentman · Answer

So yeah, june bugs were given a region and were asked to use spherical coordinates to find the volume of this region. So we&#x27;re asked to find the volume of the part of the bowl row less than or equal to a. That lies between the cones. Fi equals pi over six And Fyi equals pi over three. You saw a lot of nice parts. Now, do you? Spherical coordinates were forced to write this region using spherical coordinates? Well, we already have that row Lies between 0 & a. In the fi lies between Pi over six and pi over three theater. You can lie anywhere from 0 to 2 pi Good. And therefore we have the volume of this fall V This is the integral from state equals 0-2 pi integral from pi over six to pi over three, Integral from 0 to a. Of And then instead of devi This changes to with spherical coordinates rose squared times the sine of five zero defy the data. Then using 307 Diabetes therapy. Right? This is a product of integral. He gets the integral from 0 to 2 pi D. Theta times the integral from pi over six to pi over three. Uh Sign five, defy times the integral from zero to a. Of rho squared zero. Mhm. Taking anti derivatives. This is data from data equals 0-2 pi times negative. Co sign five from phi equals pi over six to pi over three times. Rho cubed over three. From bro equals zero to a time every state and evaluating this is two pi times. Let&#x27;s see this is negative. Sure. Co sign of pi over three is one half plus. The coastline of pi over six is route 3/2 times A cubed over three. This simplifies to Route 3 -1 times 1 3rd pie. A cute yes. So if you&#x27;re going to have some

Amy Jiang · Answer

Okay, so we&#x27;re asked Find volume O r sine x skirt. So that&#x27;s just from jail pie in a row from pie time. Sign back, squared the X. Okay, so we know the integral of sine squared of axis 1/2 times X minus one. Have science X and then evaluated up. Hi, Joe. If you evaluate this, you get this is equal to pi squared over two.

Melissa Stefan · Answer

so we have a cylinder that contains three tennis balls. We know that the cylinder has a diameter of 2.5 inches and a height of 7.5 inches, and each tennis ball has a diameter of 2.5 inches. Were asked to find the volume of the empty space within the cylinder. To do this, we need to find the volume of the cylinder and subtract from it the volume of all three tennis balls, so three times the volume of each ball. The formula for the volume of a cylinder is pi r squared H and the formula for the volume of a ball. Remember, we&#x27;re multiplying it by three would be 4/3. Pi are cute. Now all we need to do is substitute the values for our variables. We don&#x27;t yet know what the radius is, but we do know that the diameter is equal to twice the radius. The diameter of the cylinder is the same as the diameter of each tennis ball, so the radius will be the same for both as well. 2.5 is equal to two are divide both sides by two, and we have a radius of 1.25 inches. Now we can substitute that value. PI times the radius of 1.25 squared times the height of 7.5 minus three times 4/3 pi times of radius of 1.25 Cute and I highly recommend using a calculator for this. So let&#x27;s go ahead and pop over to Dismas, where we have pi times 1.25 squared times 7.5 So that&#x27;s the volume of our cylinder, and we want to subtract from that three times the volume of each tennis ball. So three times 4/3 hi times, a radius of 1.25 Cute. And we have approximately 12.27 If we round that to the nearest 10th our volume is approximately 12.3 cubic inches.

Issa Dababneh · Answer

So in this video we are told to choose the best coordinate system, uh, in order to find the volume off part of the ball given by rose less than or equal to two. That lies between these two calls. So the first thing we know is our rope. Since our fall, it is going to be less than or equal to two. The road is going to be less that are included. Two That means our role ranges from zero and we&#x27;re also given at thes. So the fees range from 54322 by over three. And finally, our data&#x27;s all of you sleep of 0 to 2. Okay, so now to find the volume is just a triple integral of volume element. The volume element is given by Rose Square, Stein et Road Sita. And now there&#x27;s just arrange the limits correctly. We know that our robos from 0 to 2, our fee goes for pi over 3 to 2 pi over three and finally our data goes from 0 to 2 parts. So we&#x27;re gonna take the integral of roads where sci fi with respect to rose that sci fi is a constant with respect to row so we can get to the side. The integral of sine Sophy Square is the cube divided by three on our limits of integration are from zero to we plug in our limits of integration. We get a thirds minus zero, which is just eight thirds. That&#x27;s a constant we can pull to the outside. So now we have a tell the double Integral have signed fee. So the integral of sine feeling perspective fees just negative. Co signed fee on our limits of integration are from flyover created to buy over three. We plug those in, so the co signed off. Two pi over three is negative. One half. But remember, we have a minus here. So becomes plus one half minus. Um, co signer high over three is negative one, but minus of the negative. Yes. Oh, co sign of pi over three. I&#x27;m story is one half, but that we have one half. We have a minus becomes negative one half and minus negative. One half becomes plus one half. So here we have simply one. All right, so we have eight birds. The integral data, the integral teeth Data&#x27;s just data data on the limit is from 0 to 2 pi with blood those in we get eight thirds times to par minus zero or a third stops to pie, which is 16 birds times pi, So the volume is 16 3rd times.

Problem

Find the indicated volumes by integration. A comm…

Problem 37 Easy Difficulty

Find the indicated volumes by integration.
The ball used in Australian football is elliptical. Find its volume if it is $275 \mathrm{mm}$ long and $170 \mathrm{mm}$ wide.

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