Question

A cylindrical ice-cream container of radius 14 cm and height 20 cm contains ice-cream upto $\frac{11}{20}$ of its height. If ice-cream from the container is filled into the ice-cream cones consisting of the cone surmounted by a hemisphere. The common radius of the cone and hemisphere is 3.5 cm and the total height of ice-cream cone (consisting hemisphere) is 7.5 cm, then the number of cones filled are

• A. 110
• B. 124
• C. 48
• D. 168

Answer 1

The correct option is C 48


Given that ice-cream is filled upto $\frac{11}{20}$ of the height of the cylindrical container.

∴ Height of ice-cream filled in cylinder $=\frac{11}{20}\times 20=11cm$

The common radius of the cone and hemisphere is 3.5 cm and total height of ice-cream cone is 7.5 cm. So, the height of conical part in the ice-cream cone will be (7.5 – 3.5) = 4 cm.

∴ Volume of the ice-cream cone = Volume of cone + Volume of hemisphere

Number of ice-creams cones $=\frac{\text{Volume of ice-cream in the cylinder}}{\text{Volume of cone + Volume of hemisphere}}$

$=\frac{\pi \left(14{)}^2\right(11)}{\frac{1}{3}\times \pi \times \left(3.5{)}^2\right(4)+\frac{2}{3}\pi (3.5{)}^3}$

$=\frac{\pi \times (14{)}^2\times (11)}{\frac{1}{3}\pi \times (49+85.75)}$

$=\frac{3\times 196\times 11}{134.75}=48$

Therefore, 48 cones can be filled.

Hence, the correct answer is option (c).