A small pizza has a diameter of 10 inches. A slice had a central angle of π/3 radians. What is the area of the slice?

The area of the slice is 13.0899 inch².

Explanation:

The pizza has an angle of 360°. If each slice has a central angle of π/3 = 60° then the number of slices = = = 6 slices. So the pizza has 6 slices.To calculate one slice's area, we calculate the the entire pizza's area and divide it by 6 (number of slices).The circle's area is given by multiplying π with the square of its radius (r²). If the diameter is 10 inches, the radius is half i.e. the radius = 5 inches.The area of the pizza = π × 5 × 5 = 78.5398 inch².                                                   The area of the slice = = 13.0899 inch².

Explanation:

In an elliptical orbit , the angular momentum of the planet remains constant because velocity of planet makes a right angle to the direction to the star .

mvr = constant .

mv₁r₁ = mv₂r₂

v₁r₁ = v₂r₂

v₁ x 21 = 38 x 75

v₁ = 135.71 km/s .