Question 1: A cuboid water tank is long, wide and deep. How many liters of water can it hold?

Answer:

Dimension of a cuboid tank:

Length Breadth Height

Therefore Volume

Question 2: A cubical vessel is long and wide. How high must it be made to hold cubic meters of a liquid?

Answer:

Dimension of a cuboid tank:

Length Breadth Height

Therefore

Question 3: Find the cost of digging a cuboid pit long, broad and deep at the rate of .

Answer:

Dimension of a cuboid pit:

Length Breadth Height

Cost of digging

Question 4: If is the volume of a cuboid of dimensions and is its surface area, then prove that

Answer:

Volume

Surface area

Dimensions are

Therefore … … … … … i)

… … … … … ii)

Dividing ii) by i) we get

Hence Proved.

Question 5: The areas of three adjacent faces of a cuboid are and . If the volume is , Prove that .

Answer:

Area of adjacent faces

Let the dimensions be Length Breadth Height

Therefore

Also … … … … … i)

… … … … … ii)

… … … … … iiii)

Multiplying i), ii) and iii) we get

. Hence proved.

Question 6: If the areas of three adjacent faces of a cuboid are , and . Find The volume of the cuboid

Answer:

Area of adjacent faces

Let the dimensions be Length Breadth Height . Given

… … … … … i)

… … … … … ii)

… … … … … iiii)

Multiplying i), ii) and iii) we get

Therefore

Question 7: The breadth of a room is twice its height; one half of its length and the volume of the room is . Find its dimensions.

Answer:

Let the dimensions be Length Breadth Height

Volume

Therefore

Therefore dimensions will be Length Breadth Height

Question 8: A river deep and wide is flowing at the rate of km per hour. How much water will fall into the sea in a minute?

Answer:

Dimension of River: Depth and Width

Velocity of rate of flow

Therefore volume of water flowing in a minute

Question 9: Water in a canal wide and deep, is flowing with a velocity of km per hour. How much area will it irrigate in minutes if of standing water is desired?

Answer:

Dimension of Canal: Depth and Width

Velocity

Therefore volume of flow in 30 minutes

Therefore area irrigated

Question 10: Three metal cubes with edges and respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.

Answer:

Total volume of the three cubes

Therefore dimension of new cube

Therefore volume

Surface area

Diagonal

Question 11: Two cubes, each of volume are joined end to end. Find the surface area of the resulting cuboid.

Answer:

Volume of cube

Therefore dimension of the cuboid

Length Breadth Height

Therefore total surface are

Question 12: Half cubic meter of gold-sheet is extended by hammering so as to cover an area of hectare. Find the thickness of the gold-sheet.

Answer:

Volume of gold

1 hectare

Let the thickness of the gold sheet

Therefore

Question 13: A metal cube of edge is melted and formed into three smaller cubes. If the edges of the two smaller cubes are and , find the edge of the third smaller cube.

Answer:

If is the dimension of the third cube

Volume of big cube

Therefore

Question 14: The dimensions of a cinema hall are and . How many persons can sit in the hall, if each Person requires of air.

Answer:

Dimension of a the hall:

Length Breadth Height

Space required by each person is

Therefore no of people that can sit in the hall

Question 15: Given that of marble weighs , the weight of marble block in width and thick is . Find the length of the block.

Answer:

Dimension of a the hall:

Length Breadth Height

Volume of the marble block

Therefore

Question 16: A box with lid is made of thick wood. Its external length, breadth and height are and respectively. How much cubic cm of a liquid can be placed in it? Also, find the volume of the wood used in it.

Answer:

External dimension of a the box:

Length Breadth Height

Thickness of the wood

Internal dimension of a the box:

Length Breadth Height

Internal Volume

External Volume

Therefor Volume of wood used

Question 17: The external dimensions of a closed wooden box are . The Box is made of thick wood. How many bricks of size can be put in this box?

Answer:

External dimension of a the box:

Length Breadth Height

Thickness of the wood

Internal dimension of a the box:

Length Breadth Height

Internal Volume

Volume of the brick

Hence the number of bricks

Question 18: How many cubic centimeters of iron are there in an open box whose external dimensions are , and , the iron being thick throughout? If of iron weighs , find the weight of the empty-box in kg.

Answer:

External dimension of a the box:

Length Breadth Height

Thickness of the wood

Internal dimension of a the box:

Length Breadth Height

External Volume

Internal Volume

Volume of Iron

Weight of Iron box

Question 19: A cube of edge is immersed completely in a rectangular vessel containing Water. If the dimensions of the base are and , find the rise in water level in the vessel.

Answer:

Volume of cube

Therefore rise in water

Question 20: A rectangular container, whose base is a square of side , stands on a horizontal table, and holds water up to, from the top. when a cube is placed in the water it is completely submerged, the water rises to the top and of water overflows. Calculate the volume of the cube and also the length of its edge.

Answer:

Dimension of a the box:

Length Breadth Height

Let the dimension of the cube

Volume of water over flowing

Therefore

Question 21: A field is long and broad. There is a plot, long and broad, near the field. The plot is dug deep and the earth taken out is spread evenly on the field. By how many meters is the level of the field raised? Give the answer to the second place of decimal.

Answer:

Dimension of field: Length Breadth

Dimension of plot: Length Breadth

Depth of dig

If is the rise in the level of the ground

Therefore

Question 22: A field is in the form of a rectangle of length and width . A pit, long, broad and deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.

Answer:

Dimension of field: Length Breadth

Dimension of pit: Length Breadth Depth

Volume of mud

Area of field

Area of pit

Therefore the area of spread

Let be the raise in the eight

Therefore

Question 23: A rectangular tank is long and broad. Water flows into it through a pipe-whose cross-section is , at the rate of . How much the level of the water rises in the tank in .

Answer:

Dimension of tank base: Length Breadth

Rate of flow of water

Volume of water flow per minute

Therefore in minutes, let be the rise in water level.

Therefore

Question 24: Water in a rectangular reservoir having base is deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side , if the water runs through the pipe at the rate of .

Answer:

Dimension of the reservoir:

Length Breadth Height

Rate of flow of water

Therefore time to empty the tank

Question 25: A village having a population of requires liters of water per head per day. It has a tank measuring . For how many days will the water of this tank last?

Answer:

Dimension of the tank:

Length Breadth Height

Volume of water required daily

Therefore the number of days the water will last

Question 26: A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in the adjoining figure. If the edge of each cube is , find the volume of the structure built by the child.

Answer:

Number of blocks

Volume of one block

Volume of the structure

Question 27: A godown measures . Find the maximum number of wooden crates each measuring that can be stored in the godown.

Answer:

Dimension of the godown:

Length Breadth Height

Dimension of the crate:

Length Breadth Height

Therefore the number of wooden crates that can be stored

Question 28: A wall of length was to be built across an open ground. The height of the wall is and thickness of the wall is . If this wall is to be built up with bricks whose dimensions are , how many bricks would be required?

Answer:

Dimension of the wall:

Length Breadth Height

Dimension of the brick:

Length Breadth Height

Therefore the number of bricks needed

Question 29: If the volume of a cube is , its surface are is and the length of a diagonal is meters, prove that

Answer:

Volume of the cube

Surface are of the cuber

Diagonal

Let the side of the cube

Therefore

Therefore

. Hence proved.

Question 30: The adjoining figure shows a victory stand, each face of which is rectangular. All measurements are in centimeters. Find its volume and surface area.

Answer:

Volume

Total surface area Front area Back area top area side area

Question 31: Water is being filled in an aquarium at the rate of liters per minute. If the aquarium is long and wide and it is filled in minutes, find the height of the aquarium.

Answer:

Dimension of the aquarium:

Length Breadth Height

Therefore flow in 90 minutes

Therefore