1. The radius of a cylinder is 5/6 its height. What is the total surface area if the volume of this cylinder is 150pi?

2. A prism and a cone have the same base area and the same height. The volume of the prism is 1. What is the volume of the cone?

3.In the diagram,  lines xy and  x'y' are diameters of the two bases of the cylinder, and  line xy is parallel to line x'y'. We know [XYY'X']=30  Find the lateral surface area of the cylinder.


4. A  circular 288 degree sector with radius 15 is rolled to form a cone. Find the height of the cone.

5. The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V cubic units and the total surface area of the frustum be A square units. Find V+A. 

6. The volume of regular octahedron PABCDQ is 243. Rotating octahedron PABCDQ about its diagonal line PQ the path of the octahedron forms a new 3D shape. What is the volume of this 3D shape?

 Apr 21, 2019

\(V = 150\pi\\ \pi r^2 h = 150\pi\\ \pi \left(\dfrac{5h}{6}\right)^2 h = 150\pi\\ \dfrac{25h^3}{36} = 150\\ h = \sqrt[3]{\dfrac{150\cdot 36}{25}} = 6\\ r = \dfrac{5h}{6} = 5\\ \text{Total surface area} = 2\pi r (r + h) = 2\pi (5)(5+6) = 110\pi\)

 Apr 21, 2019

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