The perimeter of a rectangle becomes __________ times its original perimeter, if its length and breadth are doubled.
If the diagonal d of a quadrilateral is doubled and the heights h1 and h2 falling on d are halved, then the area of quadrilateral is __________.
The surface area of a cylinder which exactly fits in a cube of side b is
__________.
The volume of a cylinder which exactly fits in a cube of side a is
__________.
The curved surface area of a cylinder is reduced by ____________ per cent if the height is half of the original height.
The volume of a cylinder becomes __________ the original volume if its radius becomes half of the original radius.
¼ times
Explanation:
Volume of cylinder = pr2h (when radius is r and height is “h”)
When the radius is halved, then it becomes
V = p (r/2)2h
V = ¼ (pr2h)
If a cube fits exactly in a cylinder with height h, then the volume of the cube is __________ and surface area of the cube is __________.
If the diagonals of a rhombus get doubled, then the area of the rhombus becomes __________ its original area.
4 times
Explanation:
Let p and q be the two diagonals of the rhombus
We know that area of a rhombus = pq/2
If the diagonals are doubled, we will get
A= (4p)(4q)/2
Take 4 outside, we will get
A = 4(pq/2)
The surface area of a cuboid formed by joining two cubes of side a face to face is __________
10a2
Explanation:
Let “a” be the side of two cubes.
When the two cubes are joined face to face, the figure obtained should be a cuboid having the same breadth and height. As the combined cube has a length twice of the length of a cube.
It means that l = 2a, b = a and h = a
Hence, the total surface area of cuboid = 2(lb + bh + hl)
= 2(2a × a + a × a + a × 2a)
Simplify the above expression, we get
= 2[2a2 + a2 + 2a2]
= 10a2
A cube of side 5 cm is cut into 1 cm cubes. The percentage increase in volume after such cutting is __________.
No change
Explanation:
Volume of cube = 53 = 125
Now, when the cube is cut into 1 cubic cm, we will get 125 small cubes
Therefore, the volume of the big cube = volume of 125 cm with 1 cubic cm.
It means that, there is no change in the volume.
Science (7568)
Maths (4467)
Technology (240)
English (170)
Grades