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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- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
