Question : An inverted conical–shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and the radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius $\frac{1}{2}$ cm are dropped in the vessel, 25% water is overflowed. The number of balls is:
Option 1: 100
Option 2: 400
Option 3: 200
Option 4: 150
Latest: SSC CGL 2024 final Result Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: 100
Solution : Given: Height of the vessel = 8 cm Radius = 5 cm. Volume of the conical vessel = $\frac{1}{3}\pi r^2 h$ = $\frac{1}{3}\times \pi\times 5^2\times 8$ = $\frac{200}{3}\pi$ cm$^3$ The volume of 25% of water = $\frac{1}{4}\times\frac{200}{3}\pi=\frac{50}{3}\pi$ cm$^3$ The volume of the spherical metallic ball of the radius $R = \frac{4}{3} \pi R^3$ $=\frac{4}{3}\times \pi\times (\frac{1}{2})^3=\frac{\pi}{6}$ cm$^3$ The number of balls required = $\frac{\frac{50}{3}\pi}{\frac{\pi}{6}}$ = 100 Hence, the correct answer is 100.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm2) of the third ball?
Option 1: $50 \pi$
Option 2: $\frac{25}{4} \pi$
Option 3: $25 \pi$
Option 4: $\frac{25}{2} \pi$
Question : A conical vessel, whose internal radius is 20 cm and height is 27 cm, is full of water. If this water is poured into a cylindrical vessel with an internal radius of 15 cm, what will be the height to which the water rises in it?
Option 1: 16 cm
Option 2: 10 cm
Option 3: 12 cm
Option 4: 14 cm
Question : Three solid metallic spheres of radii 1 cm, 6 cm, and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere formed is:
Option 1: 9.0 cm
Option 2: 5.9 cm
Option 3: 7.7 cm
Option 4: 8.5 cm
Question : A conical vessel (solid) is made of iron. Its base radius is 7 cm and its height is 15 cm. If the weight of the iron per cubic centimetre is 15 g, what is the weight of the vessel?
Option 1: 13.55 kg
Option 2: 12.55 kg
Option 3: 14.55 kg
Option 4: 11.55 kg
Question : A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are $\frac{3}{2}$ cm and 2 cm, respectively. Find the diameter of the third ball.
Option 1: 2.1 cm
Option 2: 3.3 cm
Option 3: 3 cm
Option 4: 2.5 cm
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile