The radius of the base of a hollow cone is 8, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the radius of the base of the cone be $R = 8\, cm$ and the height be $H = 15\, cm$.The slant height $L$ of the cone is given by $L = \sqrt{R^2

Vedclass · Accepted Answer

$5:3$

Vedclass · Answer

(A) Let the radius of the base of the cone be $R = 8\, cm$ and the height be $H = 15\, cm$.The slant height $L$ of the cone is given by $L = \sqrt{R^2 + H^2} = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\, cm$.Let $r$ be the radius of the largest sphere that can be inscribed in the cone.The formula for the radius of the inscribed sphere in a cone is $r = \frac{R \cdot H}{R + L}$.Substituting the values: $r = \frac{8 \cdot 15}{8 + 17} = \frac{120}{25} = 4.8\, cm$.We need to find the ratio of the radius of the base of the cone $(R)$ to the radius of the sphere $(r)$:Ratio $= R : r = 8 : 4.8$.To simplify,multiply both sides by $10$: $80 : 48$.Divide by $16$: $80/16 : 48/16 = 5 : 3$.Thus,the ratio is $5:3$.

The radius of the base of a hollow cone is $8\, cm$ and its height is $15\, cm$. $A$ sphere of the largest possible radius is placed inside the cone. What is the ratio of the radius of the base of the cone to the radius of the sphere?

Similar Questions

The cost of paint is ₹ $36/kg$. If $1\, kg$ of paint covers $1.5\, m^2$,how much will it cost to paint the outside of a cube having a $2.5\, m$ side?

$A$ rectangular sheet of area $264 \text{ cm}^2$ and width $11 \text{ cm}$ is rolled along its breadth to make a hollow cylinder. The volume of the cylinder is (in $\text{cm}^3$):

The areas of three consecutive faces of a cuboid are $12 \, cm^2$,$20 \, cm^2$,and $15 \, cm^2$. Then the volume (in $cm^3$) of the cuboid is:

$A$ conical vessel of base radius $2 \ cm$ and height $3 \ cm$ is filled with kerosene. This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius $2 \ cm$. The kerosene level in the jar is.....$cm$

The radius of the base of a conical tent is $5 \, m$. If the tent is $12 \, m$ high,then the area of the canvas required to make the tent is (in $\pi \, m^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module