Surface Area of a Frustum
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The curved surface area of a frustum of a cone is π(r1+r2)l, where l=√h2+(r1+r2)2 r1 and r2 are the radii of the two ends of the frustum and h is the vertical height.
A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. [Take π=22/7.]
A rectangular tank with a square base, an open-top, and a volume of ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let be the length of one of the sides of the square base and let be the surface area of the tank. Write the objective function.
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
(a) 1 : 3
(b) 1 : 2
(c) 2 : 1
(d) 3 : 1