Question: 26 -
If the side of a square is equal to the diameter of a circle, what is the area of the square if the area of the circle is 81π sq. cm?
-
384
-
324
-
350
-
456
Answer:
324
Solution:
Area of the circle = 81π sq. cm.
π × radius2 = 81π
Radius = 9 cm
Diameter of circle = 9 *2= 18 cm
Now, Diameter of circle = Side of the square = 18 cm
So, Area of the square = Side2 = 182 = 324 sq. cm.
Area of the circle = 81π sq. cm.
π × radius2 = 81π
Radius = 9 cm
Diameter of circle = 9 *2= 18 cm
Now, Diameter of circle = Side of the square = 18 cm
So, Area of the square = Side2 = 182 = 324 sq. cm.
Question: 27 -
What is the area of the largest circle that can be drawn inside a square of side 20 cm?
-
95 π
-
90 π
-
100 π
-
110 π
Answer:
100 π
Solution:
The diameter of the largest circle that can be drawn inside a square = length of the side of the square
As per the question: The side of the square = 20 cm.
So, radius of the circle = 20/2 = 10 cm
Area of a circle = π × radius2
The area of the largest circle = π × 102 = 100 π cm2
The diameter of the largest circle that can be drawn inside a square = length of the side of the square
As per the question: The side of the square = 20 cm.
So, radius of the circle = 20/2 = 10 cm
Area of a circle = π × radius2
The area of the largest circle = π × 102 = 100 π cm2
Question: 28 -
The diameter of a circle is increased by 100%. What is the percentage increase in area?
-
400
-
200
-
300
-
250
Answer:
300
Solution:
Let the diameter = d
Original area = π * (d/2) 2 = π d2/4
New Area = π * (2d/2) 2
= π (2d/2) (2d/2)
= π d2
Increase in area = (π d2 - π d2/4) = 3 π d2 / 4
Percentage increase = (increase in area/ original area) * 100
= (3 π d2 / 4) * (4/ π d2) * 100
= 300 %
Let the diameter = d
Original area = π * (d/2) 2 = π d2/4
New Area = π * (2d/2) 2
= π (2d/2) (2d/2)
= π d2
Increase in area = (π d2 - π d2/4) = 3 π d2 / 4
Percentage increase = (increase in area/ original area) * 100
= (3 π d2 / 4) * (4/ π d2) * 100
= 300 %
Question: 29 -
The perimeter of a circle and an equilateral triangle are equal. Find the area of the equilateral triangle if the area of the circle is 141π.
-
271.34
-
261.34
-
281.34
-
251.34
Answer:
271.34
Solution:
The perimeter of a circle and an equilateral triangle are equal:
Let the length of each side of equilateral triangle = A
As per the questions, the perimeters are equal.
So, 2 π r = 3 A
Area of circle is given = 141 π
So, π r2 = 144 π
r = 12
Thus, 2 π * 12 = 3 A
A = 24 π /3
The area of a equilateral triangle = (√3/4) * side2
= (√3/4) * (24 π /3) 2
= (√3/4) * 8 π * 8 π
= 0.43 * 25.12 * 25.12
= 271.34 sq. cm.
The perimeter of a circle and an equilateral triangle are equal:
Let the length of each side of equilateral triangle = A
As per the questions, the perimeters are equal.
So, 2 π r = 3 A
Area of circle is given = 141 π
So, π r2 = 144 π
r = 12
Thus, 2 π * 12 = 3 A
A = 24 π /3
The area of a equilateral triangle = (√3/4) * side2
= (√3/4) * (24 π /3) 2
= (√3/4) * 8 π * 8 π
= 0.43 * 25.12 * 25.12
= 271.34 sq. cm.
Question: 30 -
One of the four angles of a rhombus is 90 degrees. If each side of the rhombus is 20 cm, what will be the length of the longer diagonal?
-
20 √2
-
26 √2
-
30 √2
-
25 √2
Answer:
20 √2
Solution:
A rhombus with one of its angle 90 degrees is a square. So, both the diagonals are of equal length.
Now, Diagonal of a square= √2 × side
Given Side = 20 cm
So, Diagonal = 20 √2 cm
A rhombus with one of its angle 90 degrees is a square. So, both the diagonals are of equal length.
Now, Diagonal of a square= √2 × side
Given Side = 20 cm
So, Diagonal = 20 √2 cm