Question : The radius of a large solid sphere is 14 cm. It is melted to form 8 equal small solid spheres. What is the sum of the total surface areas of all 8 small solid spheres? (use $\pi=\frac{22}{7}$)
Option 1: 3648 cm2
Option 2: 4928 cm2
Option 3: 4244 cm2
Option 4: 4158 cm2
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: 4928 cm 2
Solution : Given: The radius of a large solid sphere is 14 cm. The volume of the sphere of radius $r$ is $\frac{4}{3}\times \frac{22}{7}\times r^3$. Its total surface area is $4\times \frac{22}{7}\times r^2$. The volume of a large solid sphere is $\frac{4}{3}\times \frac{22}{7}\times (14)^3=11499$ cm 3 . It is melted to form 8 equal small solid spheres $=\frac{11499}{8}=1437.4$ cm 3 . The volume of one sphere is 1437.4 cm 3 . $\frac{4}{3}\times \frac{22}{7}\times r^3=1437.4$ ⇒ $r^3=343$ ⇒ $r=7$ cm The sum of the total surface areas of all 8 small solid spheres $8 × 4\times \frac{22}{7}\times 7^2=4928$ cm 2 . Hence, the correct answer is 4928 cm 2 .
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : A solid metallic sphere of radius 4 cm is melted and recast into spheres of 2 cm each. What is the ratio of the surface area of the original sphere to the sum of the surface areas of the spheres, so formed?
Question : The radius of a solid sphere is 42 cm. It is melted to form identical small solid spheres whose radius is 7 cm. What is the number of small solid spheres obtained?
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 hollow sphere has an outer radius of 6 cm and inner radius of 3 cm. What is the volume of this hollow sphere?
Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm2. If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile