Problem 15
A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.
Problem 12
A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum?
Problem 9
What should be the shape of a rectangular field of a given area, if it is to be enclosed by the least amount of fencing?
Problem
Find the area of the regular six-pointed star inscribed in a circle of radius 20 cm.
Problem
Two circles as shown below are tangent to each other at point C. If AB = 9 cm and DE = FG = 5 cm, find the area of the shaded region.
Problem
Find the area of the regular five-pointed star inscribed in a circle of radius 20 cm.
Central angle = Angle subtended by an arc of the circle from the center of the circle.
Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle.
Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by
if and only if both angles intercepted the same arc. In the figure below, θ and α intercepted the same arc AB.
The following are short descriptions of the circle shown below.
The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by
where At is the area of the inscribed triangle.
The radius of incircle is given by the formula
where At = area of the triangle and s = semi-perimeter.
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