Question These questions are dealing with "solids" of geometry.
There's a lot of questions, I hope you can answer them!
1. Do you know the lateral area of a right circular cone if the diameter of the base is 4 m and the slant height of the cone is 15m? What's the solution to finding the answer?
2. What is the volume of a right pyramid whose base is a square with a side 6 m long and whose altitude is equal to the base side? Would I multiply 6 x 6 to get the correct answer?
3. How do I find the lateral area of a right cylinder if the radius of the base is 12 mm and the altitude of the cylinder is 5 times the base radius?
4. What's the surface area of a cylindrical ring if its outside diameter is 16 mm and its inside diameter is 10 mm?
5. Ok, The lower base of a frustum is a square 8 ft on each side. The upper base is a square 4 ft on each side. The altitude is 6 ft. How would I find the slant height?
6. Would the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in., whose upper base is a square with a side 3 in., and whose altitude is 12 in. be 196 cu in.?
Thank you for your time, I really appreciate you helping me! I really appreciate you reading all this and helping explain the problems and solutions.
Answer 1) If d = 4, 2r = d => r = d/2 = 4/2 = 2.
The height h is 15, so take 15c, where c is the length of the perimeter of that circle.
The length of the perimiter is c = 2(pi)r = 4pi.
The answer, then, is 15*4pi.
2) The area of the bae is 36, the height is 6, so the volume is 36*6=216.
3) Since we have r = 12, h = 5r = 5(12) = 60.
The circumference is 2(pi)r.
The area A = 5(pi)(12)(60) = 3699pi.
4) If the surface were flat:
The sureface area of the top of a circle is pi*r^2.
Calclulate the area of the circle with the big radius and subtract off the value of the circle with the small radius (the area cut out in the middle).
If you want the top and bottom, multiply by two.
However, I believe the surface is a circular cylinder. I don't know how to calculate that.
5) The volume is the difference between two cones, one of height 12 feet and base 8 ft on a side and the other with height 6 feet, 4 ft on a side. The volume of a cone is pi*A/3, where A is the surface area.
6) If the lower base is 5 in. and the upper base is 3., the height of this cone is 5/2 the height. The altitude is 12, so the cone is 30. The volume would be 30*5^2 - 18*3^2.
That is, 750 - 172 = 578.
