A cone has a base area of 20m square and a volume of 160m cube. Find the height of the cone. (please guide step by step)
Answers
Answer:
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Step-by-step explanation:
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Solution!!
The base area and volume of the cone is given in the question. We have to find the height of the cone. So first things first, we need to find the radius of the base.
Area of the base = πr²
The base area of the cone = 20 m² (Given)
20 m² = (22/7) × r²
20 m² × (7/22) = r²
r² = 70/11 m²
Now that we have the radius, we can find out the height easily.
Volume = (1/3)πr²h
The volume = 160 m³ (Given)
160 m³ = (1/3) × (22/7) × (70/11 m²) × h
160 m³ = (1/3) × (22) × (10/11 m²) × h
160 m³ = (1/3) × (2) × (10 m²) × h
160 m³ = 20/3 m² × h
h = 160 m³ × (3/20 m²)
h = 160 m × (3/20)
h = 8 m × 3
h = 24 m
The height of the cone is 24 m.