A sand timer consists of two cones joined at the apex. Each cone has height h, radius r and an
angle at the apex of 60.
a Express the radius of the top cone in terms of its height. Give your answer in exact form.
b Write the volume of the top cone as a function of its height.
c When the timer is turned over, the sand starts pouring from the top cone into the bottom
one at a constant rate of 1
32 cm3/s. Find the rate of change of the depth of the sand in the
top cone when the depth is 0.8 cm.

Question

A sand timer consists of two cones joined at the apex. Each cone has height h, radius r and an 
angle at the apex of 60. 
a Express the radius of the top cone in terms of its height. Give your answer in exact form. 
b Write the volume of the top cone as a function of its height. 
c When the timer is turned over, the sand starts pouring from the top cone into the bottom 
one at a constant rate of 1 
32 cm3/s. Find the rate of change of the depth of the sand in the 
top cone when the depth is 0.8 cm.

anonymous · Answer

Please help me Express the radius of the top cone in terms of its height!