Question

The volume of a right circular cone is 6856 cm? If the diameter of the base is 28 cm, find (i)
height of cone (ii) slant height of cone
(iii) Curved surface area of cone.
​

Answer 1

Answer:

Given:

r=

2

28

=14cm

(i)Let height =h

⇒Volume =9856=

3

1

πr

2

h

9856=

3

1

×

7

22

×14×14×h

⇒h=48cm

(ii)⇒Slant height =

r

2

+h

2

=

14

2

+48

2

=

196+2340

=50cm

(iii)⇒Curved Surface Area =πrl=

7

22

×14×50cm

2

=22004cm

2

Answer 2

QUESTION :

The volume of a right circular cone is 6856 cm³. If the diameter of the base is 28 cm, find

(i)height of cone

(ii) slant height of cone

(iii) Curved surface area of cone.

__________________________

SOLUTION :

Given :

volume of a right circular cone = 6856 cm³

Diameter of the base of circular cone = 28 cm

To find :

• height of cone
• slant height of cone
• Curved surface area of cone

Formula used :

1. Radius = d/2

2. volume of cone = 1/3 π r² h

3. slant height = √(h²+r²)

4. Curved surface Area = 2π l

where :-

• r = radius
• h= height
• l = slant height of cone
• d = diameter

Procedure :

Now it is given that :-

Diameter (d) of the base of circular cone = 28 cm

To find radius of base of circular cone , use the formula :-

⟹ Radius = d/2

⟹ Radius = 28/2

⟹ Radius = 14 cm

Now , It is given that :-

volume of a right circular cone = 6856 cm³

We will Use the formula :-

⟹ volume of cone = 1/3 π r² h

⟹ 6856 cm³ = 1/3 (22/7)(14)² h ......(put π = 22/7)

⟹ 6856 cm³ = 1/3× 22/7 ×14 × 14×h

⟹( 6856 × 3)/(22×2×14)= h

⟹ ( 3428 × 3)/(22×14)= h

⟹ (1714 × 3)/(22×14)= h

⟹ (1714 × 3)/(11×14)= h

⟹ 5142 / 154 = h

⟹ 771 / 77 = h

⟹10.01 cm = h ( approx)

TO FIND SLANT HEIGHT (l) USE THE GIVEN FORMULA :-

slant height (l)= √(h²+r²)

⟹ √((10.01)²+(14)²)

⟹ √(100.2001+196)

⟹ √(296.2001)

⟹ 17.21 ( approx)

Now we know ,

Curved surface Area = 2π l

⟹ 2 (22/7) (17.21)

⟹ 2 (22/7) (1721/100)

⟹ (2×22×1721)/(100×7)

⟹ (2×22×1721)/700

⟹ 75724/700

⟹ 108.17

ANSWER :

height of cone = 10.01 cm

slant height of cone = 17.21 cm

Curved surface Area = 108.17 cm²

____________________________

LEARN MORE:-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

______________________