Find the Surface Area and the Volume of a hemisphere Cylinders, Cones, and Spheres?

Question

http://img143.imageshack.us/img143/2391/712cylindersconesandsphot4.jpg

Answer 1

LucaPacioli's cone formulas are wrong. The surface area of a cone is found by: A = pi*r^2 + pi*r*h = pi*r (r + h).
The volume of a cone is found by V = (1/3)*pi*r^2*h

To answer the 2 questions, first the cone question:
The cone has h = height = 12cm
the diameter = 10 cm, so r = radius = 5cm
surface area = pi*r (r + h) = 3.14 * 5 (5 + 12) = 3.14 * 5 * 17
= approx. 267 square cm

hemisphere question:
The volume of a sphere is (4/3)*pi*r^3, so the volume of half a sphere is (2/3)*pi*r^3
In this question, the diameter is 17cm, so r =radius = 8.5cm
V = (2/3) * pi * (8.5cm)^3 = (2/3) * 3.14 * 614.125 cubic cm
V = 1286.22 cubic cm

Answer 2

Surface area of sphere = 4 pi R**2 where R = radius
Volume = (4/3) pi R**3

Hemisphere = 1/2 sphere
Area = (1/2)4pi R**2 + pi R**2 because must add area of circular piece at base of hemisphere = 2.5 pi R**2

Vol hemisphere= (2/3)pi R**3

Cylinder: area = 2 pi R**2 + 2 pi R H; H = height of cylinder
Cylinder vol = pi (R**2 ) H

Vol cone with R= radius of bottom and H = height =
pi (R**2) H

Surface area cone = pi R**2 + piR SQRT (H**2 + R**2)

Answer 3

i don't comprehend your argument. although, think of of a rubber circle, radius r, so as that its area is pi*r^2. Now think there is a few way of stretching it up right into a hemisphere. for sure its area might desire to be extra advantageous than pi*r^2. And it would desire to be under the area of a a million/2-dice, 2r by utilising 2r by utilising r, which might merely enclose it, i.e. it would desire to be under 4r^2 + 8r^2 = 12 r^2. the easily area, 2 pi r^2, is a little extra advantageous than a million/2 this, which seems authentic attempting to me. do you comprehend any calculus? the upward thrust in the area of a circle for an extremely tiny boost in the radius is the circumference prolonged by utilising the upward thrust in radius. On calculus concepts, this boost is comparable to the by-manufactured from the area prolonged by utilising the upward thrust in radius, meaning the circumference is the by-manufactured from the area. 2*pi*r is the by-manufactured from pi*r^2. Stepping up one measurement, the exterior area of a sphere is the by-manufactured from the quantity. 4*pi*r^2 is the by-manufactured from (4/3)*pi*r^3. this does not teach something, even though it shows how the the final option formulation extra healthful right into a advantageous development. And, talking of kinds, the quantity of a cone is one occasion of the conventional theory that the quantity of any pyramid or cone shape (i.e. flat base, with facets sloping right this moment as much as a minimum of one vertex) is (a million/3)*(area of base)*(peak) To me, that sounds like the 3-dimensional version of the two-dimensional rule that area of triangle = (a million/2)*(length of base)*(peak)