Advertisements
Advertisements
Question
The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.
Advertisements
Solution
The height of the frustum cone is h= 12 cm. The radii of the bottom and top circles are r1 = 12cm and r2 = 3cm respectively.
The slant height of the frustum cone is
`l=sqrt((r_1-r_2)^2+h^2`
`=sqrt((12-3)^2+12^2`
`=sqrt(225)`
= 15 cm
The total surface area of the frustum cone is
`=pi(r_1+r_2)xxl+pir_2^2+pir_2^2`
`=pixx(12+3)xx15+pixx12^2+pixx3^2`
= π x 225 x 26 + 144π + 9π
= 378π cm2
Hence Total surface area = 378π cm2
The volume of the frustum cone is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(12^2+12xx3+3^2)xx12`
`=1/3xxpixx189xx12`
= 756π cm3
Hence Volume of frustum = 756π cm3
APPEARS IN
RELATED QUESTIONS
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)
In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
If the surface areas of two spheres are in ratio 16 : 9, then their volumes will be in the ratio ______.
Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.
The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is ______.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
