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CA Geometry: Area, circumference, volume

31-35, area, circumference and volume. Created by Sal Khan.

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• how do you find circumference? still a little lost.
• 2 pi r, you multiply the radius times two and then multiply your product by pi.
pi= 3.14159...ect.
use pi as, 3 or 3.14.
• Cant you just use the special right triangles theorem/postulate? The one about
45-45-90 triangles, and 30-60-90 triangles?
• yes, yes you can.
• If I have two cubes of the same exact figure, (volume,area,etc.) would one fit inside the other?
• Can you tell me were you found that information? I want to look at it more in depth.
(1 vote)
• ok i get the problems and such but when i go to take like a test or something i can never recognize what i'm supposed to do to find the answer. for example for the problem where you had to subtract the triangles from the rectangle i paused the video and was thinking that i had to find the missing sides of the triangle tto get the answer... ik fail but i need help
• How do you find the volume of a sphere? I am very much confused.
• This is the formula for the volume of a sphere:
v = 4/3πr^3
• Where can you get more of the CST questions at? I think these questions are great to practice with if you are preparing to join a competitive mathmatical environment like I am. I would really appreciate a copy of a link to these problems. For now, I will just use these videos. Thank you very much, Sal, for posting these competition math and test preparation math problems!
• At I didn't exactly understand what the rhombus part was.
• a rhombus is kinda like a squished square. it has 4 sides that are all the same length. the sides that are across from each-other are parallel. the angles that are across from eachother are congruent.
hope that helped❀
• Question: The diameter of a wheel is 4. How many complete revolutions will the wheel make if it rolls a distance of 100.5pi?
• If the diameter of a wheel is 4, the circumference of the wheel is 4pi.

The wheel will make a complete revolution every time it rolls a distance of 4pi units. Thus, to find how many complte revolutions it makers after rolling 100.5pi units, we must divide 100.5pi by 4pi.
100.5pi/4pi=25 1/8
Since you said complete revolutions, we should omit the 1/8 of a revolution.

Thus, a wheel with a diameter of 4 units will make 25 complete revolutions if it rolls 100.5pi units.

• Thank you for posting video's it really helps people that need to see the big picture.
• I'm a liitle lost on how he did the equation of the area on number 35 and how he got the answer, little help ??
• `Area of triangle = (1/2)*base * height`

He showed that the triangle was a 30-60-90 triangle.

In a 30-60-90 triangle, the longest side (across from the 90 degree angle) is 2 times the length of the shortest side (across from the 30 degree angle).
In this problem, the longest side of the triangle is 12, so the shortest side = `6`. This side is the `base` of the triangle.

Also in a 30-60-90 triangle, the side across from the 60 degree angle has a length which is sqrt(3)*(shortest side)
In this problem, the shortest side is 6, so the side across from the 60 degree angle is sqrt(3)* (6) = `6sqrt(3)`. This side is the `height` of the triangle.

Area of triangle = (1/2)*base*height
= (1/2)*6*6sqrt(3)
= 3*6sqrt(3)
= 18sqrt(3)
(1 vote)