Question

The radius of a metallic sphere is 7 cm . if it melted and mold in some cones of radius 7 cm and height of 4 cm , then how many cones will be produced ?

Answer 1

Gɪᴠᴇɴ

Radius of sphere = 7 cm.

Radius of cone = 7 cm.

Height of cone = 4 cm.

Tᴏ ꜰɪɴᴅ

How many cones will be produced

Sᴏʟᴜᴛɪᴏɴ

Formulas used here :

⟼ Volume of sphere = 4/3 × (πr³)

⟼ Volume of cone = ⅓ × (πr²h)

⟼ Number of cones = Volume of Sphere/Volume of cone

Now finding volume of sphere :

⇒ Volume of sphere = 4/3 × (22/7 × 7³)

⇒ Volume of sphere = 4/3(22 × 49)

⇒ Volume of sphere = 4/3 × 1078

⇒ Volume of sphere = 4312/3

⇒ Volume of sphere = 1437.33 cm³

Now finding volume of cone :

⇒ Volume of cone = ⅓(22/7 × 7² × 4)

⇒ Volume of cone = ⅓(22 × 28)

⇒ Volume of cone = ⅓(616)

⇒ Volume of cone = 205.33 cm³

Now finding number of cones produced :

⇒ Number of cones = 1437.33/205.33

⇒ Number of cones = 7

Tʜᴇʀᴇꜰᴏʀᴇ,

Number of cones produced is 7 .

Answer 2

Answer:-

Given :

Radius of a sphere (r) = 7 cm.

Radius of the Cone (R) = 7 cm

Height of the Cone (h) = 4 cm.

Let the number of Cones Produced be "n".

According to the Question,

Volume of Sphere = n * Volume of Cone.

→ 4/3 * πr³ = n * 1/3 * πR²h

(π , 3 are cancelled out both sides)

→ 4r³ = n*R²h

→ 4(7)³ = n * (7)² * (4)

→ 1372/196 = n

→ n = 7

Therefore, 7 Cones are Produced.