The radius of the base and height of The right circular cone are 7 cm and 24 cm respectively find the volume and total surface area of cone.
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Answers
Information provided with us :
- The radius of the base and height of a right circular cone are 7 cm and 24 cm
What we have to calculate :
- Volume and Total Surface Area of the cone?
Using Formulas :
★ Volume of cone :-
- V = ⅓ π r² h
Here,
- V is volume
- value of π is 22/7
- r is radius
- h is height
★ Total Surface Area of cone :-
- T.S.A. = C.S.A of cone + base area
So it would be,
- T.S.A. = πrl + πr²
Performing Calculations :
Here we would be first calculating the volume of cone by putting all the values in the formula.
We have,
- radius (r) is 7
- height (h) is 24
Putting the values,
➺ V = ⅓ × 22/7 × (7)² × 24
➺ V = ⅓ × 22/7 × 7 × 7 × 24
➺ V = ⅓ × 22 × 7 × 1 × 24
➺ V = ⅓ × 22 × 7 × 24
➺ V = 1 × 22 × 7 × 8
➺ V = 22 × 7 × 8
➺ V = 22 × 7 × 8
➺ V = 22 × 56
➺ V = 1232 cm³
In order to calculate the total surface area we would be finding out slant height (h) of the cone.
As we know that,
- l² = h² + r²
By using it we gets,
➺ l² = (24)² + (7)²
➺ l² = (24 × 24) + (7 × 7)
➺ l² = (576) + (49)
➺ l² = 625
➺ l = √625
➺ l = 25
- Therefore, slant height (l) is 25 cm
Finding out total surface area of the cone by putting all the values in the formula.
➺ T.S.A. = πrl + πr²
➺ T.S.A. = πr (l + r)
➺ T.S.A. = 22/7 × 7 (25 + 7)
➺ T.S.A. = 22 × 1 (25 + 7)
➺ T.S.A. = 22 (25 + 7)
➺ T.S.A. = 22 (32)
➺ T.S.A. = 22 × 32
➺ T.S.A. = 704
Therefore, total surface area (T.S.A.) is 704 cm² and volume of the cone is 1232 cm³
Answer:
Given -
Radius =7cm and height=24cm
then,
l²=h²+l²
l²= 24²+ 7²
l²=576 + 49
l² = 625
l²=√625 = 25
now,
total surface area of cone= CSA + Area of base
πrl +πr² = (22/7 ×7×25) + (22/7×7×7×)
= 704cm²
Volume of cone= 1/3πr²h
= 1/3×22/7×7×7×24
= 3696/3
= 1232
Therefore, total surface area of cone is 704sq² and volume of cone is 1232cm².