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If the width of the rectangular room is three fourth of its length and its area is \(\mathrm{600m^2}\). The difference between the length and width of the room is
Let the length of the room
Width of the room
Area
The ratio between the length and breadth of a field is 10:6. The area of the field is \(3840 \mathrm m^2\). Find the difference between the length and width of the field.
Length of the field
Breadth
Length of the field
Breadth of the field
Difference
If the area of the three adjacent faces of the room is p, q, r respectively, then the volume of air in the room is
Let the length, breadth and height be l, b, h respectively.
Then lb=p, bh=q, hl=r, lbh =
A hollow garden roller whose external diameter is 42 cm and has a length of 132 cm is made of 2 cm cast iron. Find the weight of the roller if \(1cm^3\) of iron weight 10 grams.
Volume of iron
Weight of the roller
The distance covered by a farmer around a field of 120 m length and 80 m width is
Distance = 2 × (120 + 80)
= 2 × 200 = 400 m
The length of diagonal of a square whose area is \(\mathrm{16900\ m^2}\) is
Let the side of square be xm
Diagonal
The sides of a triangle are 11 cm, 15 cm, 16 cm. The altitude to largest side is
Area of the triangle
Area
Height
If the ratio of circumference of two circles is 4:9, the ratio of their area is
A sector of \(120^o \) cut out from circle has an area of \(9\dfrac{3}{7} \) sq cm. The radius of the circle is
The ratio of the volume and surface area of a sphere of unit radius is
Volume of sphere
Surface area of sphere
Ratio
But r = 1 unit
Ratio
The volume of a cube is \(125\ \mathrm{cm^3}\). The surface area of cube is
Surface area
A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is
Length of wire
Let x be the side of the square
Area of circle : Area of the square
The length and breadth of a square are increased by \(40\%\) and \(30\%\) respectively. The area of resulting rectangle exceeds the area of the square by
Side of the square be ‘a’ unit
Area squint
Length of resulting rectangle
unit
Breadth of resulting rectangle
unit
Area of rectangle
squnit
Percentage increment in the area
The volume of a regular square pyramid with base sides 10 cm and altitude 12 cm is
The total surface area of a square pyramid with a perpendicular height of 16 cm and base edge of 24 cm.
Area of triangle
Area of square base
Total surface area = Area of the base + 4 × area of a triangular face
The area of a trapezium is \(28\ cm^2\) and one of its parallel sides is \(6\ cm\). if its attitude is \(4\ cm\) then its other parallel side is
The area of two concentric circles is \(962.5\ cm^2\) and \(1386\ cm^2\) respectively.
The width of the ring is
Width of the ring
The dimensions of the floor of a rectangular hall are 4m × 3m. The floor of the hall is to be tiled fully with 8 cm × 6 cm rectangular tiles.
The number of tiles required is
Number of tiles
A square garden measuring 8 m on a side is surrounded by a 1m wide path.
What is the area of the path?
Area of the path
How many bricks of size \(\mathrm{22\ cm \times 10\ cm \times 7\ cm}\) are required to construct a wall \(11m \) long, \( 3.5m\) high and \( 40\ cm\) thick, if the cement and sand used in the construction occupy \(\left(\dfrac{1}{10}\right)^{th} \) part of the wall?
Volume of a brick
Length of the wall = 11m=1100 cm
Height of the wall = 350 cm
Width of the wall = 40 cm
Volume of the wall
Volume of the wall occupied by the bricks
Number of bricks
If the height of a cylinder is 4 times its circumference the volume of the cylinder in terms of its circumference ‘C’ is
Volume
Volume
A piece of wire when bent to form a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of the side of the square.
Circumference
Circumference of circle = perimeter of square side
Three cubes of metal with edges 3 cm, 4cm, 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube.
Volume of new cube
Edge of the cube
Lateral surface area
Find the surface area of a cylinder with diameter of base 5 cm and height 30 cm.
Surface area
Two rectangles ABCD and DBEF are as shown in the figure. The area of rectangle DBEF in square units is
Area of rectangle ABCD and DBEF are equal a they are on same base DB.
Area of rectangle ABCD
Two cubes have their volumes in the ratio 1:8. Find the ratio of their surface areas.
A child walked 13m to cross a rectangular field diagonally. If breadth of field is 5m, its length is
The radii of the bases of two cylinders are in the ratio of 2:3 respectively and their heights are in the ratio 1:2 respectively. Find the ratio of their volume.
Between a square of perimeter 64 cm and a circle of circumference 64 cm, which figure has larger area and by how much?
Side of square
Area
Area
The rectangular field has its length and breadth in the ratio 2:3. Its area is 360 hectares. The cost of fencing it at Rs 2 per meter is
The value of BH in the following figure is
Find the number of coins 1.5 cm in diameter and 0.2 cm thick melted from a right circular cylinder whose height is 8 cm and diameter 6 cm.
Volume of cylinder
Volume of coin
Number of coins
The radius of the cylinder whose lateral surface area is \(610\ cm^2 \) and height \(6\ cm\) is
If the area of a triangle with base a is equal to area of a square of side a, the altitude of the triangle is
A cylindrical tower is 7 meters in diameter and 15 meters high. The cost of white washing its curved surface area at 75 paise per \(\mathrm m^2\) is
The radius of a cylinder is doubled but its lateral surface area is unchanged. Then its height must be
If radius is doubled, then height should be half to make the lateral surface unchanged.
The radius of the cylinder whose lateral surface area is \(520\ cm^2\) and height \(5\ cm\) is
The ratio of radii of two cylinders is \(1:\sqrt2 \) and heights are in the ratio \(3:2\). The ratio of their volume is
A letter ‘T’ shape is made by sticking together 2 cuboids. What is the total volume of the letter ‘T’ ?
Volume of upper part
Volume of lower part
Total volume
The external diameter of an iron pipe is 25 cm and its length is 20 cm. if the thickness of the pipe is 1 cm. Find the total surface area of the pipe.
Length of the pipe
Thickness of pipe
Internal radius,
Total surface area