Advertisements
Advertisements
प्रश्न
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
उत्तर
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
APPEARS IN
संबंधित प्रश्न
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
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 [take π=22/7]
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =`22/7`]
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.
A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter 4 \[\frac{2}{3}\] cm and height 3 cm. Find the number of cones so formed.
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.
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m2 is
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
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.
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
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.
There are two identical solid cubical boxes of side 7 cm. From the top face of the first cube a hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted and placed on the top of the second cube’s surface to form a dome. Find
- the ratio of the total surface area of the two new solids formed
- volume of each new solid formed.
3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.
