Okay, so your first one, number six. You have two shapes there, a cone and a circle. Now you have a full cone and a half of a circle. Let's start with the cone. The formula for the volume of a cone is πr²h/3. You have your height, that is 12, so get your paper out and plug that in. H = 12. Now, your radius is where it gets a bit tricky. Have you ever heard of the Pythagorean theorem? It's a²+b²=c². Look at the cone, but look at it like it's a two-dimensional shape. You see the triangle in the middle, ignore the rest and pretend it's only that triangle. You now have a right triangle, You know your height is 12, and by looking at the triangle adjacent to it, and know it's equal, you know that your hypotenuse (the longest side of your triangle) is 15. So plug that into the Pythagorean theorem. Now you have 12²+b²=15². Use algebra to work that out, and you're left with 9. So your radius is 9. Now plug that into your volume of a cone equation. The volume of the cone is about 1017.88. Now find the circle or sphere. The formula is 4/3πr³. Just plug in your radius and get your answer, which is 3053.63. Now cut that in half, as you've only got half a circle. Now you've got 1526.82. Now add that to the volume of your cone, and you've got your final answer. 2544.7, or about that. I used π on a calc, and not 3.14, so it might be a little different.
Do you think you can do the next one? Just look at your triangle in there. You've already got one side and a hypotenuse, so plug it into the Pythagorean theorem and get your last side. Then look at the little marks on there and you can see if places are the same. If you need help with it don't hesitate to ask. I'm staying up all night anyway. Homeschooled and behind, so I'm not going anywhere.
Area of the wall = 8 x 19 = 152 ft square
Area of the window = 4 x 5 = 20 ft square
Area of 3 windows = 20 x 3 = 60 ft square
The percent area of 3 windows from area of the wall = 60/152 or approximately .395 or 39.5%
Formula
A=bh divides by 2
SUBSTITUTE
45=b9 divided by 2
MULTIPLY/DIVIDE
You can either divide by 2 or multiply by 1/2 (gets the same answer)
9 x 1/2 = 4.5
DIVIDE
45 divides by 4.5 = 10
CHECK
A= 10 x 9 divided by 2 or multiply by 1/2 (same answer) = 45
Thus, the answer is 10.
I hope this helped you understand the process!
