A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 36 feet, but the height is yet to be determined. Find the height, h, of the silo that will result in a capacity of 14580ft^3.
quantity of the cylinder is V=pi*r^2*top quantity of the hemisphere is 4/3 * pi * r^3 So entire quantity (V) is pi*r^2*top (H) + 4/3 * pi * r^3 or V=pi*r^2*H+4/3*pi*r^3 V=pi*r^2*(H+4/3*r) V/(pi*r^2)=H+4/3*r H=V/(pi*r^2) - 4/3*r Substituting 15 for r and 11250 pi for V, H=((11250*pi)/(225*pi)) - 20 H=50-20 H=30 The cylinder is 30 ft intense. because of the fact it is likewise 30 ft extensive, a hemisphere on astounding will upload one greater 15 ft, and the topmost factor of the silo is 40 5 ft above the backside. Edit: I used the formula for the quantity of a sphere, no longer of a hemisphere. So my answer would be incorrect. ignore approximately it.
The hemispherical top and the cylinder will both have a radius (r) of 18ft. The volume of the hemisphere will be just half that of a complete sphere with that radius, which is 4π r^3/3 So the hemisphere's volume is 2π r^3/3 = 3888π The cylinder's volume is the area of its base, π r^2 times the unknown height h, or 324πh The height will be such that the volumes of the cylinder and hemisphere add up to the desired quantity. 14,580 = 3888π + 324πh Solving this, I get a height of about 2.324 feet, largely because the diameter is huge for the desired capacity.
