Volume of Solids

The dimensions of an open box are $50 \mathrm{cm}, 40 \mathrm{cm} \mathrm{and} 23 \mathrm{cm}$. Its thickness is $3 \mathrm{cm}$. If $1 \mathrm{cubic} \mathrm{cm}$ of metal used in the box weighs $0.5 \mathrm{gms}$, find the weight of the box.

 The units of Volume and Capacity are same.

Check whether the given statement is true or false.

Find the volume of the cylinder if the circumference of the cylinder is $132 \mathrm{cm}$ and height is $25 \mathrm{cm}$.

A well with inner diameter $12 m$ is dug $17 m$ deep. Earth taken out of it has been evenly placed all round it to a width of $5 m$ to form an embankment. Find the height of the embankment.

A cylindrical container $21 m$ in radius and $72 m$ high is full of water. The water is emptied into a rectangular tank  $63 m$long and $24 m$ wide. Find the height of the water level in the tank.

What length of a solid cylinder $2 cm$ in diameter must be taken to recast into a hollow cylinder of external diameter $20 cm$,$15 cm$ long and $0.25 cm$  thickness. 

When a solid metal cube is completely submerged in a cylinderical vessel containing milk, with diameter $30 cm$, the level of milk rises by $1\frac{41}{99} cm$ Find the length of edge of the metal cube.

The volume of metallic cylindrical pipe is $748 c{m}^3$ Its length is $14 cm$ and its external radius is $9 cm$ Find its thickness.

At a Rath Mela, a stall keeper in one of food stalls has a large cylindercal jar of base radius $15 cm$ filled up to a height of $32 cm$ with fruit juice. The juice is filled in small cylindrical glasses of each radius $3 cm$ upto a height of $8 cm$ and sold for $₹10$ each. How much money does the stall keeper receive by selling the juice completely?

The circumference of the base of a cylindrical vessel is $132 cm$ and its height is $25 cm$ .Find Volume of cylinder.

If the answer is k ${\text{cm}}^3$ , then write the value of k.

A closed rectangular box $40 cm$ long, $30 cm$ wide and $25 cm$ deep has the same volume as that of a cylinder tin of radius $17.5 cm$. Calculate the height of the cylindrical tin correct to $1$ decimal place.

Water flows through a cylindrical pipe of internal diameter $7 cm$ at $36 km/hr$. Calculate the time in minutes it would take to fill a cylindrical tank, the radius of whose base is $35 cm$ and height $1 m$

Earth taken out on digging a circular tank of diameter $14 m$ is spread all around the tank uniformly to a width of $3.5 m$ to form an embankment of height $8 m$. Calculate the depth of the circular tank.

Water flows through a cylindrical pipe of internal diameter $7 cm$ at $5 m/s$ . Calculate the time in minutes the pipe would take to fill an empty rectangular tank $4m\times 3m\times 2.31m$

Water flows through a cylindrical pipe of internal diameter $7 cm$ at $5$ metres per second. Calculate  the volume in litres of water discharged by the pipe in one minute.

The volume of a metal pipe whose inside diameter is $6 cm$ and whose outside diameter is $8 cm$ and is $20 cm$ long is $k c{m}^3$, then find the value of $k$.

A cylinder of base diameter $8 cm$ has a volume of $100 c{m}^3$. Find the height.

A pipe, made of metal $1 cm$ thick, has an external radius $11 cm$. If the volume of metal used in making $2.8 m$ of pipe is $k c{m}^2$, then find the value of $k$.

A rectangular paper $22 cm$ by $16 cm$ can be exactly wrapped to cover the curved surface of a cylinder of height $16 cm$ Find the volume of the cylinder.

An electric geyser is cylindrical in shape, having a diameter of $3.5 cm$ and height of $1.2 m$ Neglecting the thickness of its walls, calculate its capacity in litres.