Advertisements
Advertisements
Question
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)
Advertisements
Solution
The radii of the top and bottom circles are r1 = 20 cm and r2 = 10 cm respectively. The height of the bucket is h= 12 cm. Therefore, the volume of the bucket is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(20^2+20xx10+10^2)xx12`
`=1/3xx22/7xx700xx12`
= 8800 cm3
The slant height of the bucket is
`l=sqrt((r_1-r_2)^2+h^2)`
`=sqrt((20+10)^2+12^2)`
`=sqrt(244)`
`=2sqrt(61) cm`
The total surface area of the bucket is
`=pi(r_1-r_2)xxl+pir_2^2`
`=22/7xx(20+10)xx2sqrt(61)+22/7xx10^2`
`=(1320sqrt(61)+2200)/7xxcm^2`
`=(1320sqrt(61)+2200)/7xx100 dm^2`
The total cost of tin sheet used for making the bucket is
`=1.20xx((1320sqrt(61)+2200)/(7xx100))`
= 21.40
RELATED QUESTIONS
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per 100 sq. cm. [Use π = 3.14]
If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`
In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.\[[Use\pi = 3 . 14]\]
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
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'.
If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
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.
A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cm3, then find the weight of the wire.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
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 ______.
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 ______.
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.
Ramesh made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
