Three balls of equal radius are placed such that they are touching each other. A

Question

Three balls of equal radius are placed such that they are touching each other. A fourth smaller ball is kept such that it touches the other three.Find the ratio of the radii of smaller to larger ball.

Options:

A .

\frac{(2 - \sqrt{3})}{\sqrt{3}}

B . 3- 2

\sqrt{3}

C . 3.5

D . 4

\sqrt{5}

Answer: Option A
:
A

Option (a)

Let the centers of the large balls be x, y, z and radius R.

O is the centre of the smaller ball and radius r...

x, y, z form an equilateral triangle with side equal to 2R.

O is the centroid of this triangle.

Therefore ox=oy=oz=R+r= $\frac{2}{3}$ (height of the triangle xyz)

Height= $(\frac{\sqrt{3}}{2})$ (2R) = $\sqrt{3}$ R

Therefore R+r = $\frac{2}{3}$ ( $\sqrt{3}$ R) $\Rightarrow$ $\frac{r}{R}$ = $\frac{(2 - \sqrt{3})}{\sqrt{3}}$

Shortcut:- Using the approximation technique used in class, the radius of the bigger circle: smaller circle is close to 0.2.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. There is a ship which is moving away from an iceberg 150 m high, takes 2 mins to change the angle of elevation of the to....60∘ to 45∘. What is the speed of the ship?

Question 2. A metal cuboid with sides in the ratio of 2:4:6 is melted to form small cubes of side 2 cm. If the sum of all the edge....of the cuboid to the total surface area of the cubes.

Question 3. Two rectangles, ¨ABCD and ¨PQRS overlap each other as shown in the figure below. Also, the overlapped area (shaded reg....rectangles is same is then ratio AD : PR equals

Question 4. With no wastage, small cubes of side 3 inches are formed from a cuboid with the dimensions 2:3:9 are formed. Find the ....the cuboid to that of all of the cubes.

Question 5. Suresh is standing on vertex A of triangle ABC, with AB = 3, BC = 5, and CA = 4. Suresh walks according to the following....forever. What is the total distance that Suresh walks?

Question 6. All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is ....is the minimum total area (integral) of all its surfaces?

Question 7. In the quadrilateral ABCD, AD = DC = CB, and ADC = 100∘, ABC = 130∘. Then the measure of ACB is &#....ABC = 130∘. Then the measure of ACB is

Question 8. An isosceles right triangle is inscribed in a square. Its hypotenuse is a mid segment of the square. What is the ratio o....ratio of the square’s area to the triangle’s area?

Question 9. Two travelers start walking from the same point at an angle of 1500 with each other at the rate of 4 kmph and 3 kmph. ....3 kmph. Find the distance between them after 2 hours

Question 10. Find the distance between the incentre and the circumcentre of a triangle with circumradius 6 and inradius 2? ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers