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Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.25 inches. To the...

Question

Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.25 inches. To the nearest hundredth,a. find the volume of the regular ice cream cone.b. find the volume of the waffle cone.c. how much more ice cream fits in the waffle cone compared to the regular cone?

Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.25 inches. To the nearest hundredth, a. find the volume of the regular ice cream cone. b. find the volume of the waffle cone. c. how much more ice cream fits in the waffle cone compared to the regular cone?



Answers

Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.25 inches. To the nearest hundredth,
a. find the volume of the regular ice cream cone.
b. find the volume of the waffle cone.
c. how much more ice cream fits in the waffle cone compared to the regular cone?

In this problem. We're being asked to find the volume of a comb with the given information. So they tell us that the radius of the cone is 57 years and the height of the cone is 12.47 years. So since we're finding my own cone, that's where we're going to start. Volume equals hi. Times are squared times height divided by three times square, divided by three. You might be more familiar with Formula 1/3 pi r squared H This means the same thing because taking 1/3 of something is the same thing as dividing by three. So what we're gonna do is take the given values pulling, know where they go and use word of operations to find the answer. So for pie, we're going to plug in three 0.14 with a radius. They give us five, so five square every height were given 12 0.4, the one we're all done with that will divide our answer by three. So on the top, I'm gonna multiply 3.14 times five square times 12.4. And when I do that, I get 900 and 73 point for. And since it's a cone, I need to take that answer and divide it by three. It's once we're done, we get the volume as 324. We're going around the decimal to the hundreds place. So this is gonna be point for seven centimeters cubed since we are solving from volume. So the volume was 303 124.47 centimeters cute.

In this problem were asked to find the volume of a column that has a radius of four meters in the height of 15.2 meters. So we're going to start with the volume of a cone, the formula. So the formula for my mom cone is pie. Times are squared times the height all divided by three. You might be more familiar with the formula version that is 1/3 pi r squared age. Just remember that mathematically taking the third of something is the same thing as dividing by three. This version just makes it a little easier to put the numbers. So I'm gonna plug in 3.1 floor for pie for the radius. I'm gonna plug in for square it and for the height at plug in 15.2. And then I'll take that whole numerator and divided by three. So when I do the math on the tops with 3.14 times, four times, four times 15.2, I get 763 0.6 for a knocking around. Yet I'm going around my final answer to the hundreds place, so I'm gonna take that numerator and I'm going to divided by three. And when you do that, you get 254 and at this point have been around been around it to the hundreds place. So it rounds to 254 0.55 meters cubed because we're selling for volume and we keep our units with volume.

For this problem. We're being asked to find the volume of a street light that is in the shape of a truncated coat Truncated literally means to cut off. So what happened was the street lamp used to be a full size cone, and they cut off the tip of it to make this truncated like shape. So we're being asked to find the volume of just the land shapes of the part that was left behind after we cut off this tip of it. So if you notice the tip of it is a cone shape just like the larger comb used to be. So to find the volume off just this piece, we're gonna need to find the volume of the entire comb and then take away the part that we cut off. So we're gonna take away the volume of this smaller cup. So the dimensions they give us our, uh, that the smaller cone has a radius a 0.5 feet, and the height of the smaller cone is 10 feet. And then we're given that the radius of the larger cone is one foot, and the height of the larger cone is 30 feet. So this is a three part problem. We're gonna find the following with a larger comb that we're gonna find the volume of the smaller cone, and then we're going to find the difference between them to figure out how much cone was left over after we cut that tip off. So let's start with the small boat. So violent cone volume equals pi times radius squared times, honey divided by three. So that's gonna be 3.14 times are radius of 0.5 squared times are height of 10 all divided by three. So when we multiply out the top and then divide by three, we get a volume of 2.62 cubic feet. Case or smaller call that we cut off was 2.6 cubic feet. Now we're going to find the volume of the large cone. This is part, too. Said this was a three part problem. So volume equals pi times the radius squared times height. I always start out by writing my formula. So I'm always making sure putting stuff in the right spot. Volume equals 3.14 times a radius of one squared times a height of 30 divided by three. And once I multiply through the top and then divide by three, I get a volume of 31 0.4 cubic fee. So there is my large cone. There is my small coal. To find the lamp, we have to do the large cone minus the small comb. So that's going to be 31.4 minus 2.62 which is going to give us a volume off the lamp of 28 0.78 cubic eight. So that's this part. The lamp is this part that I'm shading here in green. That's what we found. The volume. Also, the lamp is 28.78 cubic feet.

So we know that the volume of a cone is pi over three R squared H. But this one doesn't tell us the radius. But it does tell us the diameter. Well, diameter is just twice the radius. So if we divide 2.65 too, you should get that 1.5 inches is the radius. So now we're ready to plug that into the here and the height of 2.6 in for here. So we know that volume is pi over three times 1.3 squared times 2.6. If I do that on my calculator, I should get 4.6 inches cute.


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