Advertisements
Advertisements
Question
The diameters of three wheels are in the ratio 2 : 4 : 8. If the sum of the circumferences of these circles be 132 cm, find the difference between the areas of the largest and the smallest of these wheels.
Advertisements
Solution
Let the diameters of three wheel be
d1 = 2x ⇒ r1 = x
d2 = 4x ⇒ r2 = 2x
d3 = 8x ⇒ r3 = 4x
Now,
2πr1 + 2πr2 + 2πr3 = 132
⇒ 2π(r1 + r2 + r3) = 132
⇒ x + 2x + 4x = `66 xx (7)/(22)`
⇒ 7x = 21
⇒ x = 3cm
∴ DIfference between the areas of the largest and the smallest wheels
= πr32 - πr12
= π(4 x 3)2 - π(3)2
= 144π - 9π
= 135π
= `135 xx (22)/(7)`
= 424.29cm2.
APPEARS IN
RELATED QUESTIONS
Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD 90° and ∠BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral.
Find the area of the circle in which a square of area 64 cm2 is inscribed. [Use π = 3.14]
In the following figure, ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180° have been cut off. Calculate:
the length of the boundary of the shaded region.
In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?
From a thin metallic piece in the shape of a trapezium ABCD in which AB || CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet.
Find the area of a ring-shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.
Find the radius and circumference of a circle, whose area is :
(i) 154 cm2
(ii) 6.16 m2
The radius of a circular wheel is 42 cm. Find the distance travelled by it in :
(i) 1 revolution ;
(ii) 50 revolutions ;
(iii) 200 revolutions ;
The area of the circular ring enclosed between two concentric circles is 88 cm2. Find the radii of the two circles, if their difference is 1 cm.
