If the volume of cone is 1540cm³ and the area of its base is 154cm² then its height is
Answers
Answer :
The height of the cone = 30 cm
Given :
- Volume of the cone = 1540 cm³
- Area of it's base = 154 cm²
To find :
- Height of the cone
Solution :
Here, we are given the volume and area of the base of a cone and we need to calculate the height of the cone. So, for that firstly we will calculate the radius of the cone by using the following formula :
→ Base area of the cone = πr²
where,
- Take π = 22/7
- r denotes the radius of the cone
Substituting the given values :
→ 154 = 22/7 × r²
→ 154 × 7/22 = r²
→ 14 × 7/2 = r²
→ 7 × 7 = r²
→ 14 = r²
→ Taking square root on both the sides :
→ √14 = r
→ √(7 × 7) = r
→ ± 7 = r
As we know, the radius of cone cannot be negative. So, the negative sign will get rejected.
→ ± 7 Reject -ve = r
→ 7 = r
- Radius of the cone = 7 cm
Now, we will calculate the height of the cone by using the formula of volume of cone.
- Volume of cone = 1/3 πr²h
where,
- Take π = 22/7
- r denotes the radius of the cone
- h denotes the height of the cone
Substituting the given values :
→ 1540 = 1/3 × 22/7 × (7)² × h
→ 1540 = 1/3 × 22/7 × 7 × 7 × h
→ 1540 = 1/3 × 22 × 7 × h
→ 1540 = 154/3 × h
→ 1540 × 3/154 = h
→ 10 × 3 = h
→ 30 = h
Therefore, the height of the cone = 30 cm
Given:
- If the volume of cone is 1540cm³
- The area of its base is 154cm².
To Find:
- Height of cone
Solution:
We know that,
- Volume of cone = 1/3 πr²h
- Area of base = πr² = 154cm²
Volume of cone = 1/3 πr²h
➠ 1540 = 1/3 × 154 × H
➠ 1540/154 = 1/3 × H
➠ 10 = 1/3 × H
➠ Height = 10 × 3
➠ Height = 35 cm
∴ Height of cone is 30 cm