Question

the surface area of a solid metallic sphere is 616cm² .it is melted and recast into a cone if height 28cm . find the diameter of the base of the cone so formed. ​

Answer 1

$\bf{\huge{\underline{\boxed{\sf\orange{Answer:14\:cm}}}}}$

Given :

• Surface area of a solid metallic sphere is 616 cm²
• Sphere was melted and recast into a cone, with height 28 cm.

To Find :

• The diameter of the base of the cone.  

Formula used :

• Surface area of cone = 4πr²

$\huge\underline\green{\tt Solution:}$

Let the radius of cone be ' r '

→ Surface area of cone is also 616 cm².

So,

$616 =4\times\dfrac{22}{7}\times\:r^2$

→ 616  ×  7  = 88r²

→ 4312 = 88r²

→ $r^2 =\dfrac{4312}{88}$

→ r² = 49

→ r = √49

∴ r = 7 cm

Now,

→ Volume of solid metallic sphere = $\dfrac{4}{3}\pi\:r^2$

→ Volume of cone = $\dfrac{1}{3}\pi\:r^2\:h$

→ Volume of sphere = volume of cone

So,

$\frac{4}{3}\pi\:r^3 = \frac{1}{3} \pi R^2h\\\\=> 4r^3=R^2h\\\\=>4\times 7^3 = R^2 \times 28$

→ $1372 = R^2 × 28$

→ $R^2 =\dfrac{1372}{28}$

→ $R^2 = 49$

→ R = √49

∴ R = 7 cm

Therefore,

Diameter of cone = 7 × 2 = 14 cm

Answer : The diameter of the base of the cone is 14 cm

$\rule{200}2$