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A cylindrical tank has a radius of 5 meters and a height of 10 meters. Calculate the volume of the tank in cubic meters. Use the formula for the volume of a cylinder, \( V = \pi r^2 h \).
First, calculate \( r^2 \): \( 5^2 = 25 \).
Then, multiply by the height: \( 25 imes 10 = 250 \).
Finally, multiply by \(\pi\): \( 250 \pi pprox 785.398 \).
The volume of the tank is approximately 785.398 cubic meters.
#### 785.398
A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Determine if this triangle is a right triangle using the Pythagorean theorem.
\( 7^2 = 49 \) and \( 24^2 = 576 \), so \( 49 + 576 = 625 \).
Since both sides are equal, the triangle is a right triangle.
The sum of the first \( n \) positive integers is given by the formula \( S = rac{n(n + 1)}{2} \). If the sum is 5050, find \( n \).