Here is a frustum of a cone. The diagram shows that the frustum is made by removing a cone with height 3.4 cm from a solid cone with height 6.8 cm
and base diameter 7.6 cm.
3.4cm The frustum is joined to a solid hemisphere of diameter 7.6 cm
to form the solid S shown here. Solid S
The density of the frustum is 2.3g/cm
The density of the hemisphere is 4.6g/cm
3.4cm
3.4cm
Calculate the average density of solid S.
-7.6cm
-7.6cm
Your final line must say, Average density = ... g/cm

Total marks: 5

If f(x) = 3x2 - 2x+4 and g(x) = 5x + 6x - 8, find (f-g)(x).

Vertical angles must check all that apply

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)