Diameter and Chords

Help Questions

Math › Diameter and Chords

Questions 1 - 10

A circle has a radius of 7 inches. What is the diameter of the circle?

inches

Explanation

The diameter of a circle can be written as , where is the radius and is the diameter.

Therefore the diameter of the circle is 14 inches.

What is the ratio of any circle's circumference to its radius?

$2\pi :1$

$\pi :1$

$\pi ^{2}:1$

Undefined.

Explanation

The circumference of any circle is

$2\pi*r$

So the ratio of its circumference to its radius r, is

$\frac{2\pi*r}{r}$

$=2\pi$

What is the ratio of the diameter and circumference of a circle?

$\pi$

$2\pi$

$\frac{\pi}{2}$

Explanation

To find the ratio we must know the equation for the circumference of a circle is

$Circumference=\pi d$

Once we know the equation we can solve for the ratio of the diameter to circumference by solving the equation for $\frac{diameter}{Circumference}$

we divide both sides by the circumference giving us

$\frac{d}{\pi d}=\frac{1}{\pi }$

We now know that the ratio of the diameter to circumference is equal to .

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

$6.25\pi$

$6\pi$

$5\pi$

$25\pi$

$12.5\pi$

Explanation

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

$A=\pi (5/2)^2=6.25\pi$

What is the ratio of the diameter and circumference of a circle?

$\pi$

$2\pi$

$\frac{\pi}{2}$

Explanation

To find the ratio we must know the equation for the circumference of a circle is

$Circumference=\pi d$

Once we know the equation we can solve for the ratio of the diameter to circumference by solving the equation for $\frac{diameter}{Circumference}$

we divide both sides by the circumference giving us

$\frac{d}{\pi d}=\frac{1}{\pi }$

We now know that the ratio of the diameter to circumference is equal to .

What is the ratio of any circle's circumference to its radius?

$2\pi :1$

$\pi :1$

$\pi ^{2}:1$

Undefined.

Explanation

The circumference of any circle is

$2\pi*r$

So the ratio of its circumference to its radius r, is

$\frac{2\pi*r}{r}$

$=2\pi$

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

$6.25\pi$

$6\pi$

$5\pi$

$25\pi$

$12.5\pi$

Explanation

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

$A=\pi (5/2)^2=6.25\pi$

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

$6.25\pi$

$6\pi$

$5\pi$

$25\pi$

$12.5\pi$

Explanation

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

$A=\pi (5/2)^2=6.25\pi$

The perimeter of a circle is 36 π. What is the diameter of the circle?