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Geometry Formulas and Theorems

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Questions and Answers

What is the formula for the surface area of a sphere, given that the radius of the sphere is $r$?

The formula for the surface area of a sphere is $4πr^2$.

What is the formula for the lateral area of a prism, given that the height of the prism is $h$ and the perimeter of the base is $p$?

The formula for the lateral area of a prism is $hp$.

What is the formula for the volume of a cone, given that the radius of the base is $r$ and the height of the cone is $h$?

The formula for the volume of a cone is $\frac{1}{3}πr^2h$.

What is the formula for the area of a regular hexagon, given that the side length of the hexagon is $s$?

The formula for the area of a regular hexagon is $\frac{3\sqrt{3}}{2}s^2$. Signup and view all the answers

What is the formula for the volume of a cylinder, given that the radius of the base is $r$ and the height of the cylinder is $h$?

The formula for the volume of a cylinder is $πr^2h$. Signup and view all the answers

What is the formula for the surface area of a rectangular prism, given that the length, width, and height of the prism are $l$, $w$, and $h$, respectively?

The formula for the surface area of a rectangular prism is $2lw + 2lh + 2wh$. Signup and view all the answers

What is the formula for the lateral area of a geometric shape, given the base area and perimeter?

There is no direct formula for lateral area in the given material. However, it can be calculated using the formula for surface area, which is not provided in the given material. Signup and view all the answers

What is the value of sin θ in a right triangle with legs of length 3 and 4, and a hypotenuse of length 5?

sin θ = 3/5 Signup and view all the answers

What is the equation of a circle with center (h, k) and radius r?

(x - h)^2 + (y - k)^2 = r^2 Signup and view all the answers

What is the formula for the measure of an angle in a right triangle, given the lengths of the opposite side and the hypotenuse?

Cos θ = adjacent side / hypotenuse, or Tan θ = opposite side / adjacent side Signup and view all the answers

What is the formula for the quadratic equation, given the coefficients a, b, and c?

x = (-b ± √(b^2 - 4ac)) / 2a Signup and view all the answers

What is the symbol for the perimeter of a geometric shape, according to the provided notation?

p Signup and view all the answers