curved surface of a cone is 308cm^2 and it's slant height is 13 cm. find:
(1) radius of the base and
(2) total surface area of the cone
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curved surface of a cone is 308cm^2 and it's slant height is 13 cm. find:
(1) radius of the base and
(2) total surface area of the cone
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AnswEr :
Explanation :
We have given with the curved surface area of a cone and slant height of a cone, that is,
We need to find the radius of the base of a cone and total surface are of the cone.
So, firstly we will find the radius of the base of a cone.
As we are given with the CSA of cone and slant height of cone we know the required formula, that is,
→ CSA of cone = πrl.
Substituting the given values in the formula,
⇒ 308 = 22/7 × r × 13
⇒ 308 = 22/7 × 13r
⇒ 308 × 7 = 22 × 13r
⇒ 2156 = 22 × 13r
⇒ 2156 = 286r
⇒ r = 2156/286
⇒ r = 7.5
Hence, the radius of the base of a cone is 7.5 cm.
Now,
We will find the total surface are of the cone.
As we are given with the radius of a cone and height of a cone we know the required formula, that is,
→ TSA of cone = πr(l + r)
Substituting the given values in the formula,
⇒ TSA of cone = 22/7 × 7.5(13 + 7.5)
⇒ TSA of cone = 22/7 × 7.5 × 20.5
⇒ TSA of cone = 165/7 × 20.5
⇒ TSA of cone = 23.5 × 20.5
⇒ TSA of cone = 481.75
Hence, the total surface are of the cone is 481.75 cm².
Verified answer
Given :
⬤ Curved Surface Area of Cone is 308 cm² .
⬤ Slant Height is 13 cm .
To Find :
⬤ Radius of the Base .
⬤ Total Surface Area .
Solution :
1) Radius of the Base .
Formula Used :
Now :
308 = πrl
308 = 22/7 × r × 13
308/1 = 286r/7
308 × 7/286
1.07 × 7
7.5 (Approx.)
Therefore , The Radius of the Base is 7.5 cm .
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2) Total Surface Area .
Formula Used :
Now :
πr (l + r)
22/7 × 7.5 (13 + 7.5)
22/7 × 75/10 × (20.5)
33828/70
483.21 (Approx.)
Therefore , The Total Surface Area of Cone is 483.21 cm².