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 preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
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?
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?
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:
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.
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?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile