Solve the following subquestions. (Any two)
1) An aeroplane flying horizontally 1200 metre above the ground is
observed at an angle of elevation of 60°. After 6 seconds its angle
of elevation is observed to be 30°. Find the speed of the aeroplane
in km/hr.
2) A cylindrical ice cream pot of radius 6cm and height 21cm is full of
ice cream. The ice cream is to be filled in cones of height 12cm and
radius 3cm ice cream on the top of the cone has hemispherical shape.
How many such cones can be filled with ice cream ?
3) In AABC, BC = 6cm, ZB = 45°, and ZA = 100°. Construct AABC.
Construct a similar to AABC. Such that each of its side is th
of corresponding side of triangleABC.
Answers
Answer:
speed of aeroplanes is 831.38km/hour. (approx.)
Let us look at the answer:
Step-by-step explanation:
Let the speed of the aeroplane be x m/s.
In ΔABC, AB= 1200 m, BE= 6x and EC = y
tan 30°= 1200/ 6x+y ⇒ 1/√3 = 1200/6x+y ⇒ 6x+y = 1200√3 ....(i)
In ΔDEC , tan 60°= 1200/y ⇒ √3 = 1200/y ⇒ y = 1200/√3 .... (ii)
From (i) and (ii), 6x + 1200/√3 = 1200√3
⇒ 6x = 1200√3- 1200/√3 = 6x = 3600-1200/√3 = 2400/√3
x = 400/√3
x = 230.94 m/s = 230.94 × 18/5 km/h = 831.40 km/hr
2)The volume of cylindrical ice-cream pot = n× volume of ice-cream cone , where n = number of cones filled
π r²h = n × (1/3πr²h + 2/3 π r³)
π ×6² ×21 = n × π/3 ( 3² ×12 + 2×3³)
36×21= n × 1/3 (9×12 +27×2 )
36×21 ×3 / 162 = n
n = 14 cones