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Geometry - Circle Tangents and Solid Pipe Volume

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Geometry - Circle Tangents and Solid Pipe Volume

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Questions and Answers

A tangent of length 24 cm is drawn from a point to a circle. If the distance from the center of the circle to this point is 25 cm, what is the radius of the circle?

7 cm (correct)

12 cm

24.5 cm

15 cm

Two tangents, PA and PB, are drawn to a circle from an external point P, forming an angle of 80° at P. What is the measure of the angle ∠POA, where O is the center of the circle?

50°

80°

70°

40° (correct)

What is the formula for the area of a sector of a circle with a central angle of $\theta$ degrees and a radius of $r$?

$\frac{\theta}{720} \times 2\pi r^2$

$\frac{\theta}{360} \times \pi r^2$ (correct)

$\frac{\theta}{180} \times \pi r^2$

$\frac{\theta}{180} \times 2\pi r$

A solid cylindrical pipe has an inner diameter of 4 cm and a length of 20 cm. What is the volume of the pipe’s material, assuming it's a hollow pipe?

<p>$80 \pi \text{ cm}^3$</p> Signup and view all the answers

What is the formula for the total surface area of a sphere with a radius of $r$?

<p>$4\pi r^2$</p> Signup and view all the answers

Study Notes

Circle Tangents and Lengths

The length of a tangent from a point to a circle is 24 cm. The distance from the center of the circle to the point is 25 cm. The radius of the circle is 7 cm.
If tangents from a point to a circle make an angle of 80° then the angle formed between the segment from the center to the point and one of the tangents is 50°.
The area of a sector of a circle with angle θ and radius r is (θ/180) × πr².

Solid Pipe Volume

A solid pipe has a diameter of 4 cm and a length of 20 cm. The volume of the metal used in the pipe is 80π cm³.

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Description

This quiz covers the concepts of circle tangents, lengths, and the calculation of solid pipe volumes. You'll explore the relationships between points, tangents, and circle properties, as well as the formulas needed to find the volume of cylindrical objects. Test your knowledge on these geometric principles with practical examples.