According to the question, Length of the rectangular surface $=6m=600cm$ Breadth of the rectangular surface $=4m=400cm$ Height of the perceived rain $=1cm$ Then, Volume of the rectangular surface...
A cylindrical bucket, $32cm$ high and $18cm$ of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24cm$, find the radius and slant height of the heap.
It is given in the question that, Height of the cylindrical bucket $=32cm$ Radius of the cylindrical bucket $=18cm$ Height of conical heap $=24cm$ As we know that, Formula for volume of cylinder...
Find the volume largest right circular cone that can be cut out of a cube whose edge is $9cm$.
As per the question it is given that, The side of the cube $=9cm$ The largest cone that can be cut from cube will have the base diameter $=$ side of the cube $2r=9$ $r=9/2cm=4.5cm$ Now, Height of...
A well of diameter $3m$ is dug up to $14m$ deep. The earth taken out of it has been spread evenly all around it to a width of $4m$ to form an embankment. Find the height of the embankment.
As per the question it is given that, Diameter of the well $=3m$ Then, the radius of the well $=3/2m=1.5m$ Depth of the well (h) $=14m$ Width of the embankment (thickness) $=4m$ Therefore, the...
A well with inner radius $4m$ is dug up and $14m$ deep. Earth taken out of it has spread evenly all around a width of $3m$ it to form an embankment. Find the height of the embankment?
According to the question it is given that, Inner radius of the well $=4m$ Depth of the well $=14m$ As we know that, Formula for Volume of the cylinder $=\pi {{r}^{2}}h$ $=\pi \times {{4}^{2}}\times...
A well of diameter $2m$ is dug $14m$ deep. The earth taken out of it is evenly spread all around it to form an embankment of height $40cm$. Find the width of the embankment?
As per the question it is given that, Radius of the circular cylinder (r) $=2/2m=1m$ Height of the well (h) $=14m$ As we know that, Formula for volume of the solid circular cylinder $=\pi...
A $16m$ deep well with diameter $3.5m$ is dug up and the earth from it is spread evenly to form a platform $27.5m$ by $7m$. Find the height of the platform?
Consider the well to be a solid right circular cylinder Radius(r) of the cylinder $=3.5/2 m=1.75m$ Depth of the well or height of the cylinder (h) $=16m$ As we know that, Volume of the cylinder...
A path $2m$ wide surrounds a circular pond of diameter $40m$. How many cubic meters of gravel are required to grave the path to a depth of $20cm$?
As per the question, Diameter of the circular pond $=40m$ So, the radius of the pond $=40/2=20m=r$ Thickness (width of the path) $=2m$ As the whole view of the pond looks like a hollow cylinder. And...
A spherical ball of radius $3cm$ is melted and recast into three spherical balls. The radii of two of the balls are $1.5cm$ and $2cm$. Find the diameter of the third ball.
According to the question it is given, Radius of the spherical ball $=3cm$ As we know that, The volume of the sphere $=4/3\pi {{r}^{2}}$ Now, it’s volume (V) $=4/3\pi {{r}^{3}}$ That the ball is...
A hollow sphere of internal and external radii $2cm$ and $4cm$ respectively is melted into a cone of base radius $4cm$. Find the height and slant height of the cone.
As, per the question it is given The internal radius of hollow sphere $=2cm$ The external radius of hollow sphere $=4cm$ As we know that, Volume of the hollow sphere $4/3\pi \times \left(...
A hollow sphere of internal and external diameters $4cm$ and $8cm$ respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?
According to the question it is given that, Internal diameter of hollow sphere $=4cm$ So, the internal radius of hollow sphere $=2cm$ External diameter of hollow sphere $=8cm$ So, the external...
The diameters of the internal and external surfaces of a hollow spherical shell are $6cm$ and $10cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14cm$, find the height of the cylinder.
As per the question, Internal diameter of hollow spherical shell $=6cm$ Then, the internal radius of hollow spherical shell $=6/2=3cm=r$ External diameter of hollow spherical shell $=10cm$...
A solid cuboid of iron with dimensions $53cm\times 40cm\times 15cm$ is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are $8cm$ and $7cm$ respectively. Find the length of pipe.
Assume the length of the pipe be h cm. Formula for volume of cuboid is $V=whl$ Now, Volume of cuboid $=\left( 53\times 40\times 15 \right)c{{m}^{3}}$ Internal radius of the pipe $=7/2cm=r$ External...
A solid metallic sphere of radius $5.6cm$ is melted and solid cones each of radius $2.8cm$ and height $3.2cm$ are made. Find the number of such cones formed.
Assume the number of cones made be n It is given that, Radius of metallic sphere $=5.6cm$ Radius of the cone $=2.8cm$ Height of the cone $=3.2cm$ As we know that, Formula for volume of a sphere...
A cylindrical bucket, $32cm$ high and $18cm$ of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24cm$, find the radius and slant height of the heap.
It is given that, Height of the cylindrical bucket $=32cm$ Radius of the cylindrical bucket $=18cm$ Height of conical heap $=24cm$ As we know that, Volume of cylinder $=\pi \times {{r}^{2}}\times h$...
The surface area of a solid metallic sphere is $616c{{m}^{2}}$. It is melted and recast into a cone of height $28cm$. Find the diameter of the base of the cone so formed.
As per the question given, The height of the cone $=28cm$ Surface area of the solid metallic sphere $=616c{{m}^{3}}$ As we know that, Surface area of the sphere $=4\pi {{r}^{2}}$ Then, $4\pi...
How many coins $1.75cm$ in diameter and $2mm$ thick must be melted to form a cuboid $11cm\times 10cm\times 7cm$?
According to the question, Diameter of the coin $=1.75cm$ Then, its radius $=1.74/2=0.875cm$ Thickness or the height $=2mm=0.2cm$ As we know that, Volume of the cylinder $\left( {{V}_{1}}...
The diameters of internal and external surfaces of a hollow spherical shell are $10cm$ and $6cm$ respectively. If it is melted and recast into a solid cylinder of length of $8/3$, find the diameter of the cylinder?
As per the question given, Internal diameter of the hollow sphere $=6cm$ The internal radius of the hollow sphere $=6/2cm=3cm=r$ External diameter of the hollow sphere $=10cm$ Then, the external...
A copper rod of diameter $1cm$ and length $8cm$ is drawn into a wire of length $18m$ of uniform thickness. Find the thickness of the wire?
As, per the question, Diameter of the copper wire $=1cm$ Radius of the copper wire $=1/2cm=0.5cm$ Length of the copper rod $=8cm$ As we know that, Formula for volume of the cylinder $=\pi...
A copper sphere of radius $3cm$ is melted and recast into a right circular cone of height $3cm$. Find the radius of the base of the cone?
According to the question it is given that, Radius of the copper sphere $=3cm$ As we know that, Volume of the sphere $=4/3\pi {{r}^{3}}$ $=4/3\pi \times {{3}^{3}}$ ….. (i) The copper sphere is...
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.
Assume the radius of the big ball be $xcm$ The radius of the small ball $=x/4cm$ Let the number of balls $=n$ Then according to the question, we have Volume of n small balls $=$ Volume of the big...
The diameter of a metallic sphere is equal to $9cm$. It is melted and drawn into a long wire of diameter $2mm$ havinThe diameter of a metallic sphere is equal to $9cm$. It is melted and drawn into a long wire of diameter $2mm$ having uniform cross-section. Find the length of the wire.g uniform cross-section. Find the length of the wire.
According to the question it is given that, Radius of the sphere $=9/2cm$ Its volume will be $=4/3\pi {{r}^{3}}=4/3\pi {{\left( 9/2 \right)}^{3}}$ Then, the radius of the wire $=2mm=0.2cm$ Assume...
A solid metallic sphere of radius $10.5cm$ is melted and recast into a number of smaller cones, each of radius $3.5cm$ and height $3cm$. Find the number of cones so formed.
It is given that, Radius of metallic sphere $=R=10.5cm$ So, its volume $=4/3\pi {{R}^{3}}=4/3\pi {{\left( 10.5 \right)}^{3}}$ We also have, Radius of each cone $=r=3.5cm$ Height of each cone...
Three cubes of a metal whose edges are in the ratio $3:4:5$ are melted and converted into a single cube whose diagonal is $12\sqrt{3}cm$. Find the edges of the three cubes.
Assume the edges of three cubes (in cm) be $3x$, $4x$ and $5x$ respectively. Then, the volume of the cube after melting will be $={{\left( 3x \right)}^{3}}+{{\left( 4x \right)}^{3}}+{{\left( 5x...
How many spherical lead shots of diameter $4cm$ can be made out of a solid cube of lead whose edge measures $44cm$.
According to the question, The radius of each spherical lead shot $=r=4/2=2cm$ Volume of each spherical lead shot $=4/3\pi {{r}^{3}}=4/3\pi {{2}^{3}}c{{m}^{3}}$ Edge of the cube $=44cm$ Volume of...
How many spherical lead shots each of diameter $4.2cm$ can be obtained from a solid rectangular lead piece with dimensions $66cm\times 42cm\times 21cm$.
According to the question Radius of each spherical lead shot $=r=4.2/2=2.1cm$ The dimensions of the rectangular lead piece $=66cm\times 42cm\times 21cm$ So, the volume of a spherical lead shot...
Find the number of metallic circular discs with $1.5cm$ base diameter and of height $0.2cm$ to be melted to form a right circular cylinder of height 10 cm and diameter $4.5cm$.
It is given in the question that, Radius of each circular disc $=r =1.5/2=0.75cm$ Height of each circular disc $=h=0.2cm$ Radius of cylinder $=R=4.5/2=2.25cm$ Height of cylinder $=H=10cm$ So, the...
25 circular plates, each of radius $10.5cm$ and thickness $1.6cm$, are placed one above the other to form a solid circular cylinder. Find the curved surface area and the volume of the cylinder so formed.
Given, 250 circular plates each with radius $10.5cm$ and thickness of $1.6cm$. As the plates are placed one above the other, the total height becomes $=1.6\times 25=40cm$ As we know that, Curved...
50 circular plates each of diameter $14cm$ and thickness $0.5cm$ are placed one above the other to form a right circular cylinder. Find its total surface area.
According to the question, 50 circular plates each with diameter $14cm$ Radius of circular plates $=7cm$ Thickness of plates $=0.5cm$ We have to find the total surface area As these plates is one...
A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter $42cm$ and height $21cm$ which are filled completely. Find the diameter of the cylindrical vessel?
It is given that, The diameter of the cylinder $=$ the height of the cylinder $⇒h=2r$, where h – height of the cylinder and r – radius of the cylinder As we know that, Volume of a cylinder $=\pi...
What length of a solid cylinder $2cm$ in diameter must be taken to recast into a hollow cylinder of length $16cm$, external diameter $20cm$ and thickness $2.5mm$?
According to the question, Diameter of the solid cylinder $=2cm$ Length of hollow cylinder $=16cm$ The solid cylinder is recast into a hollow cylinder of length $16cm$, with external diameter of...
$2.2$ cubic dm of brass is to be drawn into a cylindrical wire of $0.25cm$ in diameter. Find the length of the wire?
It is given in the question that, $2.2d{{m}^{3}}$of brass is to be drawn into a cylindrical wire of Diameter $=0.25cm$ So, radius of the wire $(r)=d/2$ $=0.25/2=0.125*{{10}^{-2}}cm$ Then,...
A spherical ball of radius $3cm$ is melted and recast into three spherical balls. The radii of the two of the balls are $2cm$ and $1.5cm$ respectively. Determine the diameter of the third ball?
It is given in the question that, Radius of the spherical ball $=3cm$ As, we know that The volume of the sphere $=4/3\pi {{r}^{3}}$ Then, it’s volume (V) $=4/3\pi {{r}^{3}}$ That the ball is melted...
How many spherical bullets each of $5cm$ in diameter can be cast from a rectangular block of metal $11dm\times 1m\times 5dm$?
It is given that, A metallic block of dimension $11dm\times 1m\times 5dm$ The diameter of each bullet $=5cm$ As, we know that Formula of volume of the sphere $=4\pi {{r}^{3}}$ As, we know that,...
How many balls, each of radius $1cm$, can be made from a solid sphere of lead of radius $8cm$?
It is given in the question that, A solid sphere of radius, $R=8cm$ With this sphere, we have to make spherical balls of radius $r=1cm$ Now, assume that the number of balls made as n As, we know...