Advertisements
Advertisements
प्रश्न
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.
उत्तर
Given that, lots of spherical lead shots made from a solid rectangular lead piece.
∴ Number of spherical lead shots = `"Volume of solid rectangular lead piece"/"Volume of a spherical lead shot"` ...(i)
Also, given that diameter of a spherical lead shot i.e., sphere = 4.2 cm
∴ Radius of a spherical lead shot, r = `4.2/2` = 2.1 cm ...`[∵ "radius" = 1/2 "diameter"]`
So, volume of a spherical lead shot i.e., sphere
= `4/3 π"r"^3`
= `4/3 xx 22/7 xx (2.1)^3`
= `4/3 xx 22/7 xx 2.1 xx 2.1 xx 2.1`
= `(4 xx 22 xx 21 xx 21 xx 21)/(3 xx 7 xx 1000)`
Now, length of rectangular lead piece, I = 66 cm
Breadth of rectangular lead piece, b = 42 cm
Height of rectangular lead piece, h = 21 cm
∴ Volume of a solid rectangular lead piece i.e., cuboid
= I × b × h
= 66 × 42 × 21
From equation (i),
Number of spherical lead shots
= `(66 xx 42 xx 21)/(4 xx 22 xx 21 xx 21 xx 21) xx 3 xx 7 xx 1000`
= `(3 xx 22 xx 21 xx 2 xx 21 xx 21 xx 1000)/(4 xx 22 xx 21 xx 21 xx 21)`
= 3 × 2 × 250
= 6 × 250
= 1500
Hence, the required number of spherical lead shots is 1500.
APPEARS IN
संबंधित प्रश्न
The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.
Find the volume of the largest right circular cone that can be cut out of a cube where edgeis 9cm?
A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.
An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.
A vessel in the shape of cuboid ontains some water. If these identical spheres are immersed in the water, the level of water is increased by 2cm. if the area of base of cuboid is 160cm2 and its height 12cm, determine radius of any of spheres?
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is `2/3` of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.
`(use pi = 22/7)`
A solid consists of a circular cylinder surmounted by a right circular cone. The height of the cone is h. If the total height of the solid is 3 times the volume of the cone, then the height of the cylinder is
The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its : curved surface area.
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.
