Volume of a cone = π r² h/3

I envisioned a cone inside a cube. I only identified the necessary value to compute for the exact volume of the largest cone.

Edges of the cube is 10 inches. When the circle part of the cone is placed in the circle, the diameter would be 10 inches also. I divided it by 2 to get the value of the radius, resulting to 5 inches.

The height of the cone is also the height of the cube. Thus, it is 10 inches.

Volume of the cone = 3.14 * (5in)² * 10in/3
V = 3.14 * 25in² * 3.33 in
V = 261.405 in³ or 261.41 in³ VOLUME OF THE LARGEST CONE THAT CAN FIT IN A 10 INCH CUBE

4 0

2 years ago

One concern of a gambler is that she will go broke before achieving her first win. Suppose that she plays a game in which the pr

Ray Of Light [21]

Answer:

The probability that she wins exactly once before she loses her initial capital is 0.243.

Step-by-step explanation:

The gambler commences with $30, i.e. she played 3 games.

Let X = number of games won by the gambler.

The probability of winning a game is, p = 0.10.

The random variable X follows a Binomial distribution, with probability mass function:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2,...$

Compute the probability of exactly one winning as follows:

$P(X=1)={3\choose 1}(0.10)^{1}(1-0.10)^{3-1}\\=3\times0.10\times0.81\\=0.243$

Thus, the probability that she wins exactly once before she loses her initial capital is 0.243.

4 0

3 years ago