An archery target has three regions formed by three concentric circles as shown in Fig. 11.19. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions
Solution:
Given, an archery target has three regions formed by three concentric circles.
The diameters of the concentric circles are in the ratio 1:2:3
We have to find the ratio of the areas of three regions.
The diameter of the first circle = d
Radius = d/2
The diameter of the second circle = 2d
Radius = 2d/2 = d
The diameter of third circle = 3d
Radius = 3d/2
Area of circle = πr²
Area of first circle = π(d/2)²
= πd²/4
Area of second circle = πd²
Area of third circle = π(3d/2)²
= 9πd²/4
Area of the region enclosed between first and second circle = area of second circle - area of first circle
= πd² - πd²/4
= (4πd² - πd²)/4
= 3πd²/4
Area of the region enclosed between second and third circle = area of third circle - area of second circle
= 9πd²/4 - πd²
= (9πd² - 4πd²)/4
= 5πd²/4
Ratio of the areas of three regions = πd²/4 : 3πd²/4 : 5πd²/4
= 1 : 3 : 5
Therefore, the ratio of the areas of three regions is 1:3:5
✦ Try This: Given figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing the Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 13
An archery target has three regions formed by three concentric circles as shown in Fig. 11.19. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions
Summary:
An archery target has three regions formed by three concentric circles as shown in Fig. 11.19. If the diameters of the concentric circles are in the ratio 1: 2:3, then the ratio of the areas of three regions is 1:3:5
☛ Related Questions:
- The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the . . . .
- Area of a sector of central angle 200° of a circle is 770 cm². Find the length of the corresponding . . . .
- The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. . . . .