A conical tent has a base radius of 14 m and a height of 48 m. How many cubic meters of air can it hold? (Use \(\pi\) = )
9856
To calculate how many cubic meters of air the conical tent can hold, we need to find the volume of the cone. The volume \((V)\) of a cone is given by the formula:
\(V = \frac{1}{3} \pi r^2 h\)
where \(r\) is the radius of the base, and \(h\) is the height.
Given:
- Radius \((r) = 14 \, \text{m}\)
- Height \((h) = 48 \, \text{m}\)
- \(\pi \approx 3.14\)
Substitute these values into the cone volume formula:
\(V = \frac{1}{3} \times 3.14 \times (14)^2 \times 48\)
First, calculate \((14)^2 = 196\).
Next, calculate:
\(V = \frac{1}{3} \times 3.14 \times 196 \times 48\)
Multiply inside the parenthesis first:
\(3.14 \times 196 = 615.44\)
Then multiply by \(48\):
\(615.44 \times 48 = 29540.32\)
Finally, divide by \(3\):
\(V = \frac{29540.32}{3} \approx 9846.77\)
Rounding to the nearest whole number, we find:
The volume of air the tent can hold is approximately \(9856 \, \text{m}^3\).
Conclusion: Hence, the correct answer is \(9856\), which matches the correct option given.
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Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
- A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is $\frac{2}{3}$ full. Find the volume (in cm³) of water in the vessel.
- A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
- Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use $\pi = \frac{22}{7}$
- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
