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Five people will live in a tent. If each person requires 16 m2 of floor area and 100 m3 space for air then find the required height of the cone of the smallest size to accommodate those persons.
- a)18.75 m
- b)20 m
- c)21.75 m
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Five people will live in a tent. If each person requires 16 m2 of floo...
Let the height of the required cone be h cm
∴ Required base area = (16) × 5
= 80 cm2 = πr2
Height = h cm volume = 1/3 (πr2)h
According to given condition
Total volume required = 5 × 100 cm3 = 500 cm3
∴ Required base area = (16) × 5
= 80 cm2 = πr2
Height = h cm volume = 1/3 (πr2)h
According to given condition
Total volume required = 5 × 100 cm3 = 500 cm3
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Five people will live in a tent. If each person requires 16 m2 of floo...
To find the required height of the cone, we need to calculate the volume of the cone that can accommodate five people along with the required floor area and air space.
1. Calculate the floor area required:
Since each person requires 16 m2 of floor area, the total floor area required for five people can be calculated as:
Total floor area = 5 people * 16 m2/person = 80 m2
2. Calculate the volume of air space required:
Since each person requires 100 m3 of air space, the total volume of air space required for five people can be calculated as:
Total volume of air space = 5 people * 100 m3/person = 500 m3
3. Calculate the radius of the cone:
The floor area of a cone can be calculated using the formula:
Floor area = π * r2, where r is the radius of the cone.
Using the given floor area (80 m2), we can rearrange the formula to calculate the radius:
80 m2 = π * r2
r2 = 80 m2 / π
r2 ≈ 25.46
r ≈ √25.46
r ≈ 5.05 m
4. Calculate the height of the cone:
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r2 * h, where h is the height of the cone.
Using the given volume of air space (500 m3) and the calculated radius (5.05 m), we can rearrange the formula to calculate the height:
500 m3 = (1/3) * π * (5.05 m)2 * h
h = (500 m3 * 3) / (π * (5.05 m)2)
h ≈ 18.75 m
Therefore, the required height of the cone to accommodate five people with the given floor area and air space is approximately 18.75 m. Hence, the correct answer is option A.
1. Calculate the floor area required:
Since each person requires 16 m2 of floor area, the total floor area required for five people can be calculated as:
Total floor area = 5 people * 16 m2/person = 80 m2
2. Calculate the volume of air space required:
Since each person requires 100 m3 of air space, the total volume of air space required for five people can be calculated as:
Total volume of air space = 5 people * 100 m3/person = 500 m3
3. Calculate the radius of the cone:
The floor area of a cone can be calculated using the formula:
Floor area = π * r2, where r is the radius of the cone.
Using the given floor area (80 m2), we can rearrange the formula to calculate the radius:
80 m2 = π * r2
r2 = 80 m2 / π
r2 ≈ 25.46
r ≈ √25.46
r ≈ 5.05 m
4. Calculate the height of the cone:
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r2 * h, where h is the height of the cone.
Using the given volume of air space (500 m3) and the calculated radius (5.05 m), we can rearrange the formula to calculate the height:
500 m3 = (1/3) * π * (5.05 m)2 * h
h = (500 m3 * 3) / (π * (5.05 m)2)
h ≈ 18.75 m
Therefore, the required height of the cone to accommodate five people with the given floor area and air space is approximately 18.75 m. Hence, the correct answer is option A.
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