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