Question : The radius of the base of a hollow cone is 8 cm, and its height is 15 cm. A sphere of the largest radius is put inside the cone. What is the ratio of the radius of the base of a cone to the radius of a sphere?
Option 1: 5 : 3
Option 2: 4 : 1
Option 3: 2 : 1
Option 4: 7 : 3

Question

Question : A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm. What is the radius of the base of the cone?
Option 1: 1.63 cm
Option 2: 1.35 cm
Option 3: 1.33 cm
Option 4: 1.45 cm

21 Views

Answer 1

Correct Answer: 5 : 3

Solution : Given: The radius of the base of a hollow cone = 8 cm
Height = 15 cm
Now consider the problem in two dimensions.
Area of the triangle = $\frac{1}{2} \times$ base $\times$ height.
The inradius of the circle = $\frac{A}{s}$ , where $A$ is the area of the triangle and $s$ is the semi–perimeter of the triangle.

Using Pythagoras theorem, $(C B)^{2} = (B D)^{2} + (C D)^{2}$
$\Rightarrow (C B)^{2} = (8)^{2} + (15)^{2}$
$\Rightarrow (C B)^{2} = 64 + 225$
$\Rightarrow (C B)^{2} = 289$
$\Rightarrow (C B) = 17$ cm
Now, inradius = $\frac{A}{s}$
$A = \frac{1}{2} \times 15 \times 16$
$= 120$ cm $^{2}$
$\Rightarrow s = \frac{17 + 16 + 17}{2}$
$\Rightarrow s = 25$ cm
Inradius = $\frac{120}{25} = \frac{24}{5}$
The ratio of the radius of the base of a cone to the radius of a sphere is $8 : \frac{24}{5} = 5 : 3$
Hence, the correct answer is 5 : 3.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Popular Searches

Question : The radius of the base of a hollow cone is 8 cm, and its height is 15 cm. A sphere of the largest radius is put inside the cone. What is the ratio of the radius of the base of a cone to the radius of a sphere?Option 1: 5 : 3Option 2: 4 : 1Option 3: 2 : 1Option 4: 7 : 3

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download Careers360 App

All this at the convenience of your phone

Scan and download the app

Sign In/Sign Up

Question : The radius of the base of a hollow cone is 8 cm, and its height is 15 cm. A sphere of the largest radius is put inside the cone. What is the ratio of the radius of the base of a cone to the radius of a sphere?
Option 1: 5 : 3
Option 2: 4 : 1
Option 3: 2 : 1
Option 4: 7 : 3