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Q : 9     A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Given, Rate of water flow = Depth of river,  Width of the river,  The volume of water flowing in 1 min = Therefore, water falling into the sea in a minute =

Q : 8    A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

This is an important question. Given, Side of a solid cube =  We know, the volume of a cube of side  =   The volume of the given cube = Now, the cube is cut into 8 equal cubes of side  (let)  The total volume of these 8 cubes = Volume of the bigger cube   Therefore, the side of the new cube is  Now, we know, The surface area of a cube of side  =   The ratio between their surface...

Q : 7    A godown measures $\small 40\hspace{1mm}m\times 25\hspace{1mm}m\times 15\hspace{1mm}m$. Find the maximum number of wooden crates each measuring $1.5\hspace{1mm}m\times 1.25\hspace{1mm}m\times 0.5\hspace{1mm}m$ that can be stored in the godown.

Given, Dimensions of the godown =  Dimension of each wooden crate =  We know , Volume of a cuboid =   Volume of the godown =   Volume of the each crate=  Let number of wooden crates be   Volume of  wooden crates = Volume of the godown

Q : 6    A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring $\small 20\hspace{1mm}m\times 15\hspace{1mm}m\times 6\hspace{1mm}m$. For how many days will the water of this tank last?

Given, Dimensions of the tank = 4000 people requiring 150 litres of water per head per day The total volume of water required =  Let the number of days the water will last be  We know, The volume of a cuboid =   The volume of the water tank =  According to question, Therefore, the water in the tank will last for 3 days.

Q : 5    The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively $\small 2.5\hspace{1mm}m$ and 10 m.

Given, Length of the tank =  Depth of the tank =  Let the breadth of the tank be  We know, Volume of a cuboid =   The volume of the cuboidal tank =  We know,    Therefore, the breadth of the tank is

Q : 4    Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per $\small m^3$.

Given, Dimensions of the cuboidal pit =  We know , Volume of a cuboid =   Volume of the cuboidal pit =  Now, Cost of digging  = Rs. 30  Cost of digging  =

Q : 3    A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Let the height of the vessel be  Dimensions of the cuboidal water tank =  We know, The volume of a cuboid =   The volume of the water tank =  According to question, Therefore, the required height of the vessel is

Q : 2    A cuboidal water tank is 6 m long, 5 m wide and $\small 4.5\hspace{1mm}m$ deep. How many litres of water can it hold? ($\small 1\hspace{1mm}m^3=1000\hspace{1mm}l$)

Given, Dimensions of the cuboidal water tank =  We know, Volume of a cuboid =   Volume of the water tank =  We know,    Volume of water the tank can hold =
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