Question

Last question GN
504 cones, each of diameter 3.5 cm and height 3 cm are melted and recast into a metallic sphere.find the diameter of the sphere and hence find its surface area. [ use π = 22/7]
phirends are allowed including Domb

​

Answer 1

Step-by-step explanation:

● We can find the answer using volume and area formula of required shapes.

● The formula for the surface area of a right circular cone is SA = r² + rl.

● The formula for the volume of a right circular cone is V = (r²h)/3.

___________________________________

Solution

According to the question,

$\sf \: Volume \: of \: cone = \frac{1}{3} \pi r ^ 2 h \\ \sf \: Volume \: of \: metal \: in \: 504 \: cones \\ \sf \: = 504 \times \frac{1}{3} \times \frac{22}{7} \times \frac{3.5}{2} \times \frac{3.5}{2} \times 3$

$\sf \: Volume \: of \: Sphere = \frac{4}{3} \pi r ^ 3 \\ \sf \: = \frac{4}{3} \times \frac{22}{7} \times {r}^{3}$

Now, Volume of sphere = Volume of metal in 504 cones

$\sf \frac{4}{3} \times \frac{22}{7} \times {r}^{3} = 504 \times \frac{1}{3} \times \frac{22}{7} \times \frac{35}{20} \times \frac{35}{20} \times 3$

$\sf \: or \: {r}^{3} = ( \frac{21}{2} ) ^{3} \\ \sf \: or \: {r}^{3} = 10.5cm$

$\sf Diameter =2 \times 10.5=21 cm \\ \sf Surface \: area = 4 \pi r ^ 2$

$\sf \: = 4 \times \frac{22}{7} \times 10.5 \times 10.5 \\ \sf \red{ \underline{ = 1386 {cm}^{2} }}$

Additional Information :

• Volume of cylinder = πr²h

• T.S.A of cylinder = 2πrh + 2πr²

• Volume of cone = ⅓ πr²h

• C.S.A of cone = πrl

• T.S.A of cone = πrl + πr²

• Volume of cuboid = l × b × h

• C.S.A of cuboid = 2(l + b)h

• T.S.A of cuboid = 2(lb + bh + lh)

• C.S.A of cube = 4a²

• T.S.A of cube = 6a²

• Volume of cube = a³

• Volume of sphere = 4/3πr³

• Surface area of sphere = 4πr²

• Volume of hemisphere = ⅔ πr³

• C.S.A of hemisphere = 2πr²

• T.S.A of hemisphere = 3πr²

Hope it will help you siso ^_^

And kindly mark me brainliest ✌️

Answer 2

THEME

The story Discovering Tut: The Saga Continues, is a description of the exploration conducted by a team of researchers. It gives the account of struggles the team faces to unravel the mystery of the death of a teenage ruler, King Tut.

Tut became pharaoh of Egypt in 1332 B.C. at the age of nine. He ruled the country at a time of conflict, when battles over land raged between Egypt and the neighboring kingdom of Nubia. Nearly a decade after coming to power, the young leader died at about 18. But historians didn't know much about Tut until 1922.