S 5. A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Then the number of such cones which can be filled with ice-cream is
a.9
b.8
c.10
d11
Answers
Answer:
c
Step-by-step explanation:
The crt answer of this question is option C
For right circular cylinder
Diameter = 12 cm
Radius(R1) = 12/2= 6 cm & height (h1) = 15 cm
Volume of Cylindrical ice-cream container= mr1²h1= 22/7 x 6x6x 15=11880/7 cm³
Volume of Cylindrical ice-cream container=11880/7 cm³
For cone,
Diameter = 6 cm
Radius(r2) =6/2 = 3 cm & height (h2) = 12 cm Radius of hemisphere = radius of cone= 3 cm
Volume of cone full of ice-cream- volume of cone + volume of hemisphere
=% mr2²h2 + % mr2³= π (12³h2 +212³)
= ½ * 22/7 (37× 12 + 2× 3³)
=% * 22/7 (9x12 + 2 × 27)
= 22/21 (108 +54)
= 22/21(162)
= (22×54)/7
Let n be the number of cones full of ice cream.
Volume of Cylindrical ice-cream container=n x Volume of one cone full with ice cream
11880/7 = n* 1188/7
11880 = n * 1188
n = 11880/1188=10
n = 10
Hence, the required Number of cones = 10