Question

Find the Volume and CSA of cone whose Vertical height = 20 cm and Diameter is 14 cm​

Answer 1

Step-by-step explanation:

Given :-

Given The cone whose Vertical height =

20 cm and Diameter is 14 cm

To find:-

Find the Volume and CSA of cone whose

Vertica height = 20 cm and

Diameter is 14 cm

Solution:-

Diameter of the cone = 14 cm

Radius of the cone = Diameter/2

=>Radius of the cone = 14/2 = 7 cm

Radius of the cone = 7 cm

Vertical height of the cone = 20 cm

We know that

Slant height of a cone (l)=√{h^2+r^2} units

we have , r = 7 cm and h = 20 cm

=>Slant height = √(20^2+7^2)

=>Slant height = √(400+49)

=>Slant height = √449 cm

Now,

Curved Surface Area of a cone = πrl

sq.units

=>CSA = (22/7)×7×√449 sq.cm

=>CSA = 22√449 sq.cm

Curved Surface Area of the cone =

22√449 sq.cm

Volume of a cone =(1/3) πr^2h cubic units

=>V = (1/3)×(22/7)×(7^2)×20 cubic cm

=>V = (1/3)×(22/7)×49×20

=>V= (1×22×49×20)/(3×7)

=>V = 22×7×20/3

=>V=3080/3

=>V=1026.66666...

=>V= 1026.67 cubic cm

(Correct it two decimals)

Answer:-

Curved Surface Area of the given cone =

22√449 sq.cm

Volume of the given cone = 1026.67 cubic cm

Used formulae:-

• Slant height of a cone(l)=√{h^2+r^2} units

• Curved Surface Area of a cone = πrl sq.units

• Volume of a cone =(1/3) πr^2h cubic units

Answer 2

Given

• Vertical height of cone = 20 cm
• Diameter of cone = 14 cm

To find

• Volume of cone
• Curved surface area of cone

Solution

• Diameter = 14 cm
• Radius = Diameter/2
• Radius = 7 cm

Now, we have vertical height (h) and radius (r), and we need to find the slant height (l) of the cone in order to find volume, curved surface area.

• l² = h² + r²
• l² = 20² + 7²
• l² = 400 + 49
• l² = 449
• l = √449

Hence, the slant height of the cone is √449 cm.

Curved surface area of cone :-

• πrl
• 22/7 × 7 × √449
• 22√449

Hence, the C.S.A of cone is 22√449 cm².

Volume of cone :-

• 1/3 πr²h
• 1/3 × 22/7 × 7 × 7  × 20
• (1 × 22 × 49 × 20)/(3 × 7)
• 3080/3
• 1026.666

Hence, the volume of cone is 1026.67 cm³.