Question

the volume of a cone is 9856 CM if the diameter of its base is 28 cm what is its height and its slant height

Answer 1

HEIGHT=48 CM
SLANT HEIGHT=50CM

Answer 2

Given diameter of the base of the cone is 28cm, therefore radius is = 28/2 = 14cm

Volume of the cone = 9856cm³
Therefore 1/3πr²h = 9856cm³
=> 1/3×22/7×14×14×h = 9856cm²
=> 22/3×2×14×h = 9856cm³
=> 616/3×h = 9856cm³
=> h = 9856/1×3/616
=> h = 16×3
=> h = 48cm

Verification:-

Volume of the cone = 1/3πr²h
= 1/3×22/7×14×14×48
= 22/3×2×14×48
= 29568/3
= 9856cm³

Hence, the height of the cone is 48cm.

Now, by Pythagoras thereom we will find the slant height.

Let slant height be hypontuse.

a² + b² = c²
14² + 48² = c²
196 + 2304 = c²
2500 = c²
c = √2500
c = 50cm

Slant height of the cone is 50cm.

Hope my answer is right...