The ratio of the circumference of two circles is 5 : 8. What is the ra

1.	The ratio of the circumference of two circles is 5 : 8. What is the ratio of their corresponding areas?1. 5 : 82. 25 : 643. 64 : 254. 8 : 5
Answer» Correct Answer - Option 2 : 25 : 64 Given: The ratio of the circumference of two circles = 5 ∶ 8 Formula used: Circumference of a circle = 2 π R Area of a circle = π R² Calculations: Let the radius of two circles be r₁ and r₂ The ratio of the circumference of two circles = (2 × π × r₁) ∶ (2 × π × r₂) ⇒ r₁ ∶ r₂ = 5 ∶ 8 The radius of two circles are 5x and 8x Ratio of corresponding areas = (π × r₁²) ∶ (π × r₂²) ⇒ r₁² ∶ r₂² = (5x)² ∶ (8x)² ⇒ 25x² ∶ 64x² ⇒ 25 ∶ 64 ∴ The ratio of their corresponding areas is 25 ∶ 64

The ratio of the circumference of two circles is 5 : 8. What is the ratio of their corresponding areas?1. 5 : 82. 25 : 643. 64 : 254. 8 : 5

Answer» Correct Answer - Option 2 : 25 : 64

Given:

The ratio of the circumference of two circles = 5 ∶ 8

Formula used:

Circumference of a circle = 2 π R

Area of a circle = π R²

Calculations:

Let the radius of two circles be r₁ and r₂

The ratio of the circumference of two circles = (2 × π × r₁) ∶ (2 × π × r₂)

⇒ r₁ ∶ r₂ = 5 ∶ 8

The radius of two circles are 5x and 8x

Ratio of corresponding areas = (π × r₁²) ∶ (π × r₂²)

⇒ r₁² ∶ r₂² = (5x)² ∶ (8x)²

⇒ 25x² ∶ 64x²

⇒ 25 ∶ 64

∴ The ratio of their corresponding areas is 25 ∶ 64

Discussion

No Comment Found

Related InterviewSolutions

The dimensions of a rectangle are 24 cm and 16 cm. If the circumference of the circle is 110% of the perimeter of rectangle, then what will be the area of the circle?1. 550 cm22. 792 cm23. 616 cm24. 921 cm25. 587 cm2
Forty-two cubes each of side 1 cm are glued together to form a solid cuboid. If the perimeter of the base of the cuboid is 18cm, then its height, in cm, is1. 12. 23. 34. 4
If the area of a right-angled isosceles triangle is 676 cm2, then the length of its hypotenuse is:1. 53 cm2. 52 cm3. 50 cm4. 51 cm
The number of solid spheres ,each of diameter 3 cm that could be moulded to form a solid metal cylinder of height 54 cm and diameter 4 cm is?1. 162. 243. 364. 48
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the radius of each such ball is ___________.1. 1.25 cm2. 2.5 cm3. 3.75 cm4. 5 cm
The ratio of the length and the breadth of a rectangular plot is 6 : 5 respectively, if the breadth of the plot is 34 meters less than the length, what is the perimeter of the rectangular plot?1. 408 meters2. 814 meters3. 374 meters4. 748 meters
A rectangular swimming pool of length 30 m, breadth 25 m and 4.5 m depth is to be constructed with tiles of square shape. Find how many such tiles needed (approx) to cover the swimming pool. It is given that the side of the tiles is 40 cm1. 75642. 77653. 78624. 7781
The perimeter of the rectangle of breadth 16cm is 98cm. The area of a rectangle and curved surface area of a cylinder is the same. The difference between the height and radius of the cylinder is 5cm. Find the volume of a cylinder.1. 1848 cubic.cm2. 1526 cubic.cm3. 1330 cubic.cm4. 1240 cubic.cm5. 1642 cubic.cm
Find the length of the longest rod that can be placed in a hall of 10 m length, 6 m breadth and 4 m height.1. 2√19 m2. 2√ 38m3. 4√38 m4. 3√38 m
The side of an equilateral triangle is 15cm. The equal side of isosceles triangle is 14cm. The perimeter of isosceles triangle and equilateral triangle is same. Find the ratio of sides of an isosceles triangle.1. 18 : 15 : 152. 17 : 15 : 153. 14 : 14 : 174. 14 : 14 : 195. 17 : 17 : 14