Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The height of the frustum of the cone is h= 16 cm. The perimeters of the circular ends are 44 cm and 33 cm. Let the radii of the bottom and top circles are r1 cm and r2 cm respectively. Then, we have
2πr1= 44
⇒ πr1= 22
⇒ `r_1+(22xx7)/22`
⇒ r1 = 7
2πr2 = 33
⇒ `pi r_2=33/2`
⇒ `r_2=33/2xx7/22`
⇒ `r_2=21/4`
The slant height of the bucket is
`l=sqrt((r_1-r_2)^2+h^2)`
`=sqrt((7_21/4)^2+h^2)`
= 16.1 cm
The curved/slant surface area of the frustum cone is
`= pi(r_1+r_2)xxl`
`=(pir_1+pir_2)xxl`
= (22 + 16.5)xx16.1
= 619.85 cm2
Hence Curved surface area = 619.85cm2
The volume of the frustum of the cone is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(7^2+7xx5.25+5.25^2)xx16`
= 1900 cm3
Hence Volume of frustum = 1900cm3
The total surface area of the frustum cone is
`=pi(r_1+r_2)xxl+pi r_1^2+pi r_2^2`
`=619.85+22/7xx7^2+22/7xx5.25^2`
= 860.25 Square cm
Hence Total surface area = 860.25 cm2
APPEARS IN
संबंधित प्रश्न
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (use π 3.14).
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`]
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [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.
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
1) The area of the metal sheet used to make the bucket.
2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm2 of the surface is 10paise. Find total cost to paint the vessel all
over______?
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
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.
Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is
If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
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]`.
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
