A solid object is made in the shape of a cylinder diameter D and length L with a cone on the end base diameter?
1) Write down the formula for the volume ‘V’ and the surface area ‘A’ in
terms of D,L and H.
2) If the volume is 500,000mm cubed and the cylinder is 60mm diameter by
100mm long, what is the height of the cone?
simple answers please
I assume the height of the cone is H even though you did not state that in the question.
Volume first:
Volume of cylinder part = πDDL/4 or Pi D squared L/4
Volume of cone part = 1/12 πDDH or Pi D squared H divided by 12
Add these two together for total volume.
Surface Area:
Cylinder Part (base + curved surface)
Base = πDD/4
Curved Surface = πDL
Cone = πHL/2
Total Surface Area = πDD/4 + πDL + πHL/2
Part (2)
Calculate volume of cylinder that is 60mm Dia and 100mm Long
V = πDDL/4 = π 60*60 * 100/4 = 282743.34mm cubed
so volume of cone is 500000- 282743.34 = 217256.66 mm cubed
1/12 πDDH = 217256.66, D = 60
H = 217256.66 * 12 / (π * 60 * 60) = 230.52mm
My entry for the 60 mm base contest. INTERMEDIATE CATEGORY
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