Question : 24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 3 cm
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 6 cm
Solution : The total volume of the 24 solid hemispheres is equal to the volume of the cylinder. The volume of the cylinder = $\pi r^2h$ Volume of the cylinder (height $h$, radius $r$) = $\pi(12)^2 × 24 = 144 × 24\pi$ Since the 24 solid hemispheres have the same volume as the cylinder, the volume of each hemisphere can be calculated as: Now, equate the volume of 24 hemispheres (each having a radius equal to $R$) to the cylinder. $⇒24 × (\frac{2}{3}) \pi R^3 = 144 × 24\pi$ $⇒\frac{2}{3}R^3 = 144$ $⇒R^3 = 216$ $⇒R = 6$ Therefore, the radius of each solid hemisphere is 6 cm. Hence, the correct answer is 6 cm.
Candidates can download this e-book to give a boost to thier preparation.
Application | Eligibility | Admit Card | Answer Key | Preparation Tips | Result | Cutoff
Question : How many solid spherical balls of radius 6 cm can be made by melting a solid hemisphere of radius 12 cm?
Option 1: 4
Option 2: 2
Option 3: 10
Option 4: 8
Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Option 1: 105
Option 2: 101
Option 3: 108
Option 4: 103
Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?
Option 1: 7 cm
Option 2: 10 cm
Option 3: 9 cm
Option 4: 8 cm
Question : A metallic sphere of radius 21 cm is melted and then recast into smaller cones, each with a 7 cm radius and a height of 3 cm. Find the number of cones obtained.
Option 1: 225
Option 2: 325
Option 3: 522
Option 4: 252
Question : Two circles touch each other externally, having a radius of 12 cm and 8 cm, respectively. Find the length of their common tangent AB with point A on the bigger circle and B on the smaller circle.
Option 1: $8 \sqrt{6} \mathrm{~cm}$
Option 2: $8 \sqrt{3} \mathrm{~cm}$
Option 3: $12 \sqrt{3} \mathrm{~cm}$
Option 4: $12 \sqrt{6} \mathrm{~cm}$
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile