Digital PSAT Math Practie Test 16: Geometry and Trigonometry

1

A right circular cylinder has a volume of 30x cubic feet, and a cube has a volume of 21x cubic feet. What is the sum of the volumes of a cone with the same height and radius as the cylinder and of a pyramid with the same length, width, and height of the cube?

2

Andrew rides his bike 20 miles directly north and then 15 miles directly to the east. How many miles would he travel if he could fly directly from his starting point to his ending point?

3

In a right triangle with legs of length a and b, what is the value of the hypotenuse of the triangle?

A.

B.

C.

4

A rectangle has side lengths of 6 inches and 8 inches. What is the length of the diagonal of the rectangle?

5

What would be the measure, in radians, of an arc on a circle if the measure of the arc in degrees was 270?

A.

B.

D.

6

A circular pizza has a radius of 8 inches. If the pizza is cut into 8 equal sectors as shown in the drawing above, what is the length of the crust on the edge of each piece, rounded to two decimal places?

7

In the above drawing, lines AB and CD are parallel, and line EF is a transversal. How many angles made from the given lines measure 60 degrees?

8

A four-sided figure has three interior angles of the same measure and the other interior angle measuring 120 degrees. What is the measure of the smallest interior angle in the figure?

9

In two similar isosceles triangles, triangle A has two sides each of length 5 and one side of length 7. Triangle B has exactly one side of length 28. What is the perimeter of triangle B?

10

Triangle XYZ has a right angle for angle Y and has side lengths of 24 for XY and 26 for XZ. For a triangle that is similar to XYZ, what would be the value of the tangent of its smallest angle?

A.

B.

C.

D.