Question

(7) A sphere a cylinder and a cone have the same
radius find the ratio of their curved susface
avea​

Answer 1

GIVEN:

a sphere,cylinder and cone have same radius

TO FIND:

ratio of their curved surface area

SOLUTION:

Let "r" be the common radius of the sphere, cylinder and cone

Then,

height of cone = height of cylinder = height of sphere = 2r

Let "l" be the slant height of the cone

Then,

$\sf \: l \: = \sqrt{ {h}^{2} + {r}^{2} } = \sqrt{ {4r}^{2} + {r}^{2} } = r \sqrt{5}$

Now,

$\sf curved\: surface \: area \: of \: sphere \: = {4\pi r}^{2}$

$\sf \: curved \: surface \: area \: of \: cylinder \: = {4\pi r}^{2}$

$\sf \: curved \: surface \: area \: of \: cone \: = \pi rl = \pi r. \sqrt{ {5\pi r}^{2} } = \sqrt{\pi {r}^{2} }$

⊱ Required Ratio:

$\implies\sf \: 4\pi {r}^{2} \ratio \: 4\pi {r}^{2} \ratio \: \sqrt{5\pi {r}^{2} }$

$\implies\sf \: 4 \ratio 4 \ratio \: \sqrt{5}$

Hence,

ratio of the curved surface area of sphere, cylinder and cone is =$\sf\underline\red{4\: \ratio \: 4 \: : \sqrt{5}}$

Answer 2

$\huge\bold{\mathtt{\red{A{\pink{N{\green{S{\blue{W{\purple{E{\orange{R}}}}}}}}}}}}}$

Step-by-step explanation:

Let "r" be the common radius of the sphere, cylinder and cone

GIVEN:

Math

a sphere,cylinder and cone have same radius

5 points

TO FIND:

ratio of their curved surface area

SOLUTION:

Then,

height of cone = height of cylinder = height of sphere = 2r

Let "l" be the slant height of the cone

Then,

\sf \: l \: = \sqrt{ {h}^{2} + {r}^{2} } = \sqrt{ {4r}^{2} + {r}^{2} } = r \sqrt{5}

Now,

\sf curved\: surface \: area \: of \: sphere \: = {4\pi r}^{2}

\sf \: curved \: surface \: area \: of \: cylinder \: = {4\pi r}^{2}

\sf \: curved \: surface \: area \: of \: cone \: = \pi rl = \pi r. \sqrt{ {5\pi r}^{2} } = \sqrt{\pi {r}^{2} }

ANSWER

⊱ Required Ratio: