Question

a sphere of radius 8 cm is melted and recast into a cone of height 32 cm find CSA of the cone​

Answer 1

C.S.A. of the Cone = 6436.57 cm² .

Step-by-step explanation:

$\\ \sf \large \pink{Given}$

• Radius of Sphere = 8 cm .
• Height of Cone = 32 .
• Sphere is melted and recast into Cone .

Therefore,

$\boxed{ \sf Volume \: of \: Sphere = Volume \: of \: Cone .}$

$\sf \large \pink{To \: find}$

• C.S.A( Curved Surface Area) of the Cone .

$\\ \sf \large \pink{Formula \: used} \: \\ \\ \sf \: volume \: of \: spere \: = \dfrac{4}{3} \pi {r}^{3} \\ \\ \sf \: volume \: of \: cone \: = \dfrac{1}{3} \pi {r}^{2}$

$\sf \large \pink{Solution}$

Volume of Sphere = Volume of Cone .

So,

$\sf \: \dfrac{4}{3} \pi {r}^{3} _{(Sphere)} = \dfrac{1}{3} \pi {r}^{2}_{(Cone)} h \:$

$\\ \sf \: \dfrac{4}{ \cancel3} \cancel \pi {r}^{3}_{(Sphere)} = \dfrac{1}{ \cancel3} \cancel\pi {r}^{2}_{(Cone)} h \: \\ \\ \sf \: 4 \times 8 \times 8 \times 8 = {r}^{2} \times 32 \\ \\ \sf 2048 = {r}^{2} \times 32 \\ \\ \sf \: {r}^{2} = \dfrac{2048}{32} \\ \\ \sf \: {r}^{2} =64 \\ \\ \underline{\boxed{ \sf r \: = 8 \: cm }}$

Now, we have the value of Radius of the Cone .

We have to find the Curved Surface Area of the Cone.

Curved surface of Cone = πrl .

Here, we have

• r = 8 cm
• h = 32 cm

we have to find out the value of l (slant height)

$\sf \: l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \sf \: l = \sqrt{ {(8)}^{2} + {(32)}^{2} } \\ \\ \sf \: l = \sqrt{65536} \\ \\ \sf \: l = 256cm$

Now,

$\sf \: C.S.A. \: of \: cone \: = \dfrac{22}{7} \times 8 \times 256 \\ \\ \sf \: C.S.A. \: of \: cone \: = \dfrac{45056}{7} \\ \\ \underline{\boxed{\sf \: C.S.A. \: of \: cone \: = 6436 .57 \: {cm}^{2}}} \:$

Some Formula related to Cone and Sphere :-

• C.S.A of Cone = πrl
• C.S.A of Sphere = T.S.A of Sphere = 4πr² .
• T.S.A of Cone = πrl + πr² .
• Volume of Cone = ⅓ πr²h .
• Volume of Sphere = ⁴/₃ πr³ .