Question

the volume of right circular cone is 9856cube .If the diameter of the base is 28cm,find. height of the cone ,slant height of the cone.

Answer 1

If V be the volume of a right circular cone then,
V=1/3πr²h where r=radius of the base of the cone and h=height of the cone
Here, diameter of the base=28cm
∴, radius of the base=28/2=14cm
∴, 9856=1/3×22/7×14²×h
or, h=(9856×3×7)/(22×14×14)
or, h=48cm
Now, slant height=l=√(h²+r²)
or, l=√(48²+14²)
or, l=√(2304+196)
or, l=√2500
or, l=50cm
∴, height of the cone is 48cm and slant height of the cone is 50cm.

Answer 2

$\sf \huge \bigstar \: answer \bigstar$

Given :-

The volume of the right circular cone

= 9856cm^3

Diameter =28 cm

Radius = Diameter/2

Radius of the cone = 14cm

Solution 1 :-

Volume of the cone = 1/3πr^2h

Put the required values in the formula ,

9856 = 1/3 * 22/7 * 14 * 14 * h

h = 9856 * 3 * 7 / 22 * 14 * 14

h = 206976 / 4312

h = 48

Hence , The height of the cone is 48cm

Solution 2 :-

Radius of the cone = 14 cm

Height of the cone = 48cm

Now ,

( l )^2 = (radius)^2 + ( height )^2

Slant height ( l )^2 = √( 14)^2 + ( 48)^2

( l )^2 = 196 + 2304

( l )^2 = 2500

l = 50 cm

Thus , The slant height of a cone is 50 cm

Solution 3 :-

Total surface area of cone

Put the required values in the formula ,

TSA of cone = 22/7 * 14 ( 50 + 14)

TSA of cone = 22 * 2 * 64

TSA of cone = 2816 cm²