Listen NCERT Audio Books to boost your productivity and retention power by 2X.
The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions.
Given diameter of front wheel = d = 80 cm
so, Radius of front wheel = r = d/2 = 80/2 = 40 cm
Diameter of rear wheel = D = 2 m = 200 cm
Distance covered by wheel in 1 revolution = Circumference of wheel
⇒ Distance covered by front wheel = 2πr = 2π(40)
⇒ Distance covered by front wheel = 80π
∴ Distance covered by front wheel in 800 revolutions = 80π×800
⇒ Distance covered by front wheel in 800 revolutions = 6400π → eqn1
⇒ Distance covered by rear wheel = 2πR = 2π(100)
⇒ Distance covered by rear wheel = 200π → eqn2
Let the number of revolutions made by rear wheel to cover 6400π cm be “x”
∴ (x)×200π = 6400π (from eqn1 and eqn2)
⟹ x = 64000/200
⇒ x = 320
Number of revolution made by rear wheel to cover the distance covered by front wheel in 800 revolutions is 320.
ABCD is a field in the shape of a trapezium, AD || BC, ∠ABC = 90° and ∠ADC = 60°. Four sectors are formed with centres A, B, C and D, as shown in the figure. The radius of each sector is 14 m.
Find the following:
(i) total area of the four sectors,
(ii) area of the remaining portion, given that AD = 55 m, BC = 45 m and AB = 30 m.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [Take π = 3.14.]