Question

the sand is fulled with the cylinder of height 32cm and radius 18 cm. then it pour into the ground in the shape of inverted cone height of the sand is 24cm find the radius and slant height of the cone​

Answer 1

Answer:

the radius of cone is 36 and slant height is 43.2

if you satisfied from this answer please market is brilliant

Answer 2

$\bff{GIVEN :}$

Cylinder ;

${\bff{\purple{Radius = 32cm}}}$

${\bff{\purple{Height = 32cm}}}$

Cone ;

${\bff{\purple{Height = 24cm}}}$

To find ;

• Radius
• Slant height of c0ne

Assumption ;

Let radius be r

Let slant height be l cm

Volume of cylinder ;

$volume \: of \: cylinder \: = { \pi \: r}^{2} h$

$\implies \: \pi \: \times \: 18 \times 18 \times 32$

$10368\pi \: cm {}^{3}$

Volume of Cone ;

$volume \: of \: cone \: = \frac{1}{3\pi} {r}^{2} h$

$\implies \: \frac{1}{3} \pi \: {r}^{2} 24 \\ \\ \implies \: 8\pi \: {r}^{2}$

Since the content of cylinder is pored to conr , the Volume of Cone = Volume of Cylinder .

$10368\pi \: = \: 8\pi \: {r}^{2}$

$\frac{10368 \: \pi}{8 \: \pi} = {r}^{2}$

${r}^{2} = 1296 \\ r \: = 36$

We know ,

${l}^{2} = {h}^{2} + {r}^{2}$

${l}^{2} = 24 {}^{2} + 36 {}^{2}$

${l}^{2} = 576 + 1296 \\ {l}^{2} = \sqrt{1872} \\ {l}^{2} = 12 \sqrt{13}$