find L.S.A TSA and volume of cone who's base radiuses 5cm and the height is 12 cm
Answers
Answer:
L.S.A = 204.285
T.S.A = 282.857
Volume = 314.285
Step-by-step explanation:
GIVEN:
r = 5cm
h = 12cm
l^2 = h^2 + r^2
=12^2 + 5^2
= 144 + 25
l^2 = 169
l = 13
L.S.A of the cone = πrl sq.units
= 22/7 x 5 x 13
=22/7 x 65
= 1430 / 7
= 204.285 cm^2
T.S.A of the cone = πr(l + r) sq. units
= 22/7 x 5 ( 13 + 5)
= 110 / 7( 18)
= 1980 / 7
=282.857 cm^2
volume of the cone = 1/3π r^2h cu. units
= 1/3(22/7) 5^2 (12)
= 22/21 x 25 x 12
= 22/21 x 300
= 6600/21
= 314.285
Given:-
- Radius of base of cone = 5 cm
- Height of the Cone = 12 cm
To Find:-
- LSA of the cone
- TSA of the cone
- Volume of the cone.
Solution:-
We know,
✭ Volume of cone = 1/3 πr²h sq.units.
Hence,
Volume of cone = 1/3 × 22/7 × (5)² × 12
=> Volume of cone = 22/7 × 25 × 4
=> Volume of cone = 100 × 22/7
=> Volume of cone = 100 × 3.14
=> Volume of cone = 314.3 cm³
Hence, the volume of the cone us 314.3 cm³
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Now,
We are given with the height and radius of the cone through which we'll find the slant height of the cone.
We know,
✭ l² = r² + h²
Hence,
l² = (5)² + (12)²
=> l² = 25 + 144
=> l² = 169
=> l = √169
=> l = 13 cm
Hence,
The slant height of the cone is 13 cm
Now,
✭ Lateral Surface Area of Cone = πrl sq.units
Hence,
LSA of Cone = 22/7 × 5 × 13
=> LSA of cone = 204.3 cm²
Hence, LSA of the cone is 204.3 cm²
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Now,
✭ Total Surface Area of cone = 2πr(r + l) sq.units
Hence,
TSA of the cone = 22/7 × 5(5 + 13)
=> TSA of the cone = 22/7 × 5 × 18
=> TSA of the cone = 282.9 cm²
Hence, the TSA of the cone is 282.9 cm².
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