1.What is the difference between a Sphere, a Cone, and a Cylinder?
2.What is the difference between the formulas for these circular solids?
3.Write the formula and name the dimensions you need to know to calculate the volume of a Sphere:
5 Problems - SHOW ALL WORK!
1. Name the faces, edges, and vertices for a sphere:
2. Find the volume of the sphere: raidius 2cm
3. Find the radius of a sphere whose volume = 43π m^3.
4. A sphere that is 18 inches across has what volume?
5. Find the volume of the sphere if the volume of a cone with the same radius and h = 2r is 297 in^3 .
1. The main difference between a Sphere, a Cone, and a Cylinder is their shape. A Sphere is a perfectly round object where all points on the surface are equidistant from the center. A Cone is a circular solid with a curved surface that tapers to a point called the apex. A Cylinder is a three-dimensional object with two parallel circular bases connected by a curved surface.
2. The formulas for these circular solids are:
- Sphere: V = 4/3 πr^3
- Cone: V = 1/3 πr^2h
- Cylinder: V = πr^2h
3. Formula for calculating the volume of a Sphere:
V = 4/3 πr^3
Dimensions needed: Radius (r)
Problems:
1. Sphere does not have faces, edges, or vertices as it is a curved three-dimensional shape with no flat surfaces.
2. V = 4/3 π(2)^3 = 4/3 π(8) = 32π cm^3
3. V = 43π, Solve for r: r = (3∛(43π))/(4π) = 3 m
4. The diameter of a sphere is 18 inches, so the radius will be 9 inches. V = 4/3 π(9)^3 = 972π in^3
5. Given h = 2r, volume of the cone is V_cone = 1/3 πr^2h = 297 in^3
Substitute h = 2r into the volume formula of cone: V_cone = 1/3 πr^2(2r) = 297
Solve for r = 3
Now, use the radius value to find the volume of the sphere: V_sphere = 4/3 π(3)^3 = 36π in^3