CASE STUDY QUESTION 52-Class X-Maths

CASE STUDY QUESTION 52-Class X-Maths

In the month of December 2020, it rained heavily throughout the day over the city of Hyderabad. Anil observed the raindrops as they reached him. Each raindrop was in the shape of a hemisphere surmounted by a cone of the same radius of 1 mm. Volume of one of such drops is 3.14 mm³. Anil collected the rain water in a pot having a capacity of 1099 cm³. [Use √2 = 1.4]

Based on the above situation, answers the following questions.
(a) Find the total height of the drop.
(i) 1 mm (ii) 2 mm (iii) 3 mm (iv) 4 mm

(b) The curved surface area of the drop is

(i) 8.74 mm³ (ii) 9.12 mm³ (iii) 10.68 mm³ (iv) 12.54 mm³

(c) As the drop fell into the pot, it changed into a sphere. What was the radius of this sphere?
(i) (3/4) ^1/3
(ii) (4/3) ^1/3
(iii) 3 ^1/3
(iv) 4 ^1/3

(d) How many drops will fill the pot completely.
(i) 260000 (ii) 280000 (iii) 320000 (iv) 350000

(e) The total surface area of a hemisphere of radius r is