Question

vo
4G+
3:20 PM -
46
Q 1.
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and
recast into a sphere. The radius of the sphere is :
1) 4.2 cm
2) 2.1 cm
3) 2.4 cm
4) 1.6 cm
1. Option
2. Option
3. Option
4. Option
Answer:
1
2
3
4
Al for RouiSNext​

Answer 1

Answer:

$\bigstar{\bold{Option\:2:\:2.1\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Height of cone(h) = 8.4 cm
• Radius (r) = 2.1 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Radius of the sphere

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the volume of the cone

→ Volume of the cone is given by the formula,

  Volume of the cone = 1/3 × π × r² × h

→ Now we have to find the volume of the sphere

→ Volume of the sphere is given by

  Volume of the sphere = 4/3 × π × R³

→ By given ,

  Volume of cone = Volume of sphere

→ Substituting the values we get,

   1/3 × π × r² × h = 4/3 × π × R³

→ Cancelling 1/3 and π on both sides,

   r² h = 4 R³

→ Substituting the values,

  2.1 × 2.1 × 8.4 = 4 R³

  4 R³ = 37.044

     R³ = 37.044/4

     R³ = 9.261

     R = ∛9.261

     R = 2.1 cm

→ Hence the radius of the sphere is 2.1 cm

$\boxed{\bold{Radius=2.1\:cm}}$

→ Therefore option 2 is correct.

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Volume of a cone is given by,

   Volume of a cone = 1/3 × π × r² × h

→ Volume of a sphere is given by

   Volume of a sphere = 4/3 × π × r³