Question

Komal finds radius r of a sphere during an experiment. For this she took a cylindrical container with radius R = 7cm and height = 10 cm . She filled the container almost half by water. Now she dropped a yellow sphere in the container. She observed the water level increased from A to B equal to 3.4 cm.
1.What is the approximate radius of sphere?
(a) 4 cm (b) 6 cm (c) 5 cm (d) 2 cm
2. What is the volume of cylinder?
(a) 1240 cm³ (b) 1450 cm³ (c) 1750 cm³ (d) 1540 cm³ This is a required question
3. How many litres water can be filled in the full container?
(a) 1.24 L (b) 1.45 L (c) 1.75 L (d) 1.54 L
4. What is the diameter of the yellow sphere?
(a) 8 cm (b) 12 cm (c) 10 cm (d) 4 cm
5. What is the curved surface area of a cylinder?
(a) 2πrh (b) 2πr(r-h) (c) 2πr(r+h) (d πrl​

Answer 1

This is a tedious question but

First calculate the volume of the water filled = 1/2*pi*r^2*h

=1/2*22/7*7*7*10

=770cm^3

now level increased by 3.4 cm add 3.4cm to height = 13.4cm

now volume = 1/2*22/7*7*7*13.4 = 1031.8

change in volume = volume of sphere

1031.8-770 = 4/3*pi*r^3

r = 3.97cm

so answer for 1. is (a)

2. = 1540 (d)

3. 1540cm^3 = 1540/1000000*1000 = 1.54 L(D)

4. (a)

5. (a)