An open cuboid measures internally x units by 2x units by h units and has an inner surface area of 12 units^2.
Show that the volume, V units^3, of the cubiod is given by V(x)=2/3x(6-x^2).
Also;
A child's drinking beakeris in the shape of a cylinder with a hemispherical lid and a circular flat base. The radius of the cylinder is r cm and the height is h cm. The volume of the cylinder is 400cm^3.
Show that the surface area of plastic, A(r) needed to make the beaker is given by A(r)=3πr^2+(800/r)
Show that the volume, V units^3, of the cubiod is given by V(x)=2/3x(6-x^2).
Also;
A child's drinking beakeris in the shape of a cylinder with a hemispherical lid and a circular flat base. The radius of the cylinder is r cm and the height is h cm. The volume of the cylinder is 400cm^3.
Show that the surface area of plastic, A(r) needed to make the beaker is given by A(r)=3πr^2+(800/r)
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V = 2*(x^2)*h----------------- 1, we have
Inner surface area = 2*xh + 2*(2x*h) + 2x^2 = 12 or
h(x+2x) + x^2 = 6 or h = (6-x^2)/(3x) Substituting in1 we get
V = 2*(x^2)*{(6-x^2)/(3x)} = (2/3)x(6-x^2) (Proved)
Second problem
V = π*(r2) h = 400 or = h=400/(πr^2)
A(r) = π*r^2 + 2*π*rh + 2*π*r^2 = 3πr^2 + 2π[400/(πr) -(2/3)] = 3πr^2+(800/r)
Inner surface area = 2*xh + 2*(2x*h) + 2x^2 = 12 or
h(x+2x) + x^2 = 6 or h = (6-x^2)/(3x) Substituting in1 we get
V = 2*(x^2)*{(6-x^2)/(3x)} = (2/3)x(6-x^2) (Proved)
Second problem
V = π*(r2) h = 400 or = h=400/(πr^2)
A(r) = π*r^2 + 2*π*rh + 2*π*r^2 = 3πr^2 + 2π[400/(πr) -(2/3)] = 3πr^2+(800/r)