Find the slant height of a cone whose, (i) Base radius - 14 cm, height -0.48 m (ii) Base diameter = 70 cm, curved surface area 4070 cm​

Answer:

(i) 50cm

(ii) 37 cm

Step-by-step explanation:

Part (i) : -

Given that

Radius of cone(r) = 14cm

Height of the cone(h) = 0.48m

                                    = (0.48 × 100)cm

                                h  = 48 cm

Slant height of the cone (l) ?

We know that

l² = h² + r²

l² = 48² + 14²

l² = 2304 + 196

l² = 2500

l = √2500

l = 50 cm

Thus slant height of the cone is 50 cm

Part (ii) : -

Given that

Base diameter of cone = 70cm

Radius of cone(r) = 70/2

                         r = 35 cm

and

Curved surface area of the cone = 4070 cm

πrl = 4070

π × 35 × l = 4070

(22/7) × 35 × l = 4070

22 × 5 × l = 4070

110 × l = 4070

l = 4070/110

l = 407/11

l = 37

l = 37 cm

Thus slant height of the cone is 37 cm    

Note:-

CSA of Cone =   πrl   

• Base radius is 14 cm of a cone
• Height is 0.48 m of that cone

• Slant height (l) of the cone ?

Using formula of calculating the slant height of cone (l),

• l² = h² + r²

Here,

• l is slant height
• h is height
• r is radius

But before putting the values in it we would be changing the unit of height (h) which is in metres into centimetres.

➺ h = 0.48 × 100

➺ h = (48/100) × 100

➺ h = 48 cm

Therefore, height of cone in centimetres is 48cm.

Putting all the required values,

➺ l² = (48)² + (14)²

➺ l² = (48 × 48) + (14 × 14)

➺ l² = (2304) + (196)

➺ l² = 2304 + 196

➺ l² = 2500

➺ l = √2500

➺ l = 50

Therefore, slant height (l) of the cone is 50 cm.

_____________________________________

• Curved surface area (C.S.A) of the cone is 4070 cm.
• Diameter is of 70 cm.

• Slant height (l) of the cone.

★ Curved surface area of cone :-

• C.S.A. = πrl

Here,

• Value of π is 22/7
• r is radius
• l is slant height

First of all we would be finding out the radius of the cone as we have been provided with its diameter.

As we know that,

➺ r = d / 2

By using it we gets,

➺ r = 70 / 2

➺ r = 35

Therefore, radius of the cone is of 35 cm.

Putting all the values in the formula,

➺ 4070 = (22/7) (35) (l)

➺ 4070 = 22/7 × 35 × l

➺ 4070 = 22 × 35 × l / 7

➺ 4070 = 22 × 5 × l

➺ l = 4070 / 22 × 5

➺ l = 814 / 22

➺ l = 407 / 11

➺ l = 37

Therefore, slant height (l) of the cone is of 37cm.

★ Volume of cone:-

• V = ⅓ πr²h

★ Total Surface Area of cone:-

• T.S.A. = πrl + πr²

Some more formulas related to concept surface area and volume :

★ Curved surface area of cylinder:-

• C.S.A. = 2πrh

★ Total surface area of cylinder:-

• T.S.A. = 2πr (h + r)

★ Volume of cylinder:-

• V = πr²h

★ Area of cross-section:-

• Area of cross-section = πr²

★ Volume of sphere:-

• V = 4/3 × πr³

★ Volume of cube:-

• V = a³

In these formulas,

• r is radius
• h is height
• a is side of cube