A hemisphere and a cone have equal bases. If | vedclass

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

Question

(B) Let the radius of the base of the hemisphere be $r$ units. Since the bases are equal,the radius of the cone is also $r$ units.Given that the heigh

Vedclass · Accepted Answer

$2: \sqrt{2}$

Vedclass · Answer

(B) Let the radius of the base of the hemisphere be $r$ units. Since the bases are equal,the radius of the cone is also $r$ units.Given that the heights are equal,the height of the cone $h = r$ (as the height of a hemisphere is equal to its radius).The slant height $l$ of the cone is given by $l = \sqrt{r^2 + h^2} = \sqrt{r^2 + r^2} = \sqrt{2r^2} = r\sqrt{2}$.The curved surface area of the hemisphere is $2\pi r^2$.The curved surface area of the cone is $\pi rl = \pi r(r\sqrt{2}) = \pi r^2\sqrt{2}$.The ratio of the curved surface area of the hemisphere to the curved surface area of the cone is $2\pi r^2 : \pi r^2\sqrt{2} = 2 : \sqrt{2}$.

$A$ hemisphere and a cone have equal bases. If their heights are also equal,the ratio of their curved surfaces will be

Similar Questions

$A$ spherical aquarium can accommodate $11$ fishes,and each fish requires $1.54 \, m^3$ of water. What is the volume of the aquarium? (in $m^3$)

The area of three adjacent faces of a rectangular box are $p, q$ and $r$ square $cm$. The volume of the box is given by

The radii of a cylinder and a cone are equal. If the height of the cylinder is equal to the slant height of the cone,then the ratio of the curved surface areas of the cylinder and the cone is: (in $:1$)

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?

If the radius of a sphere is doubled,then its volume is increased by (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module