Volume of Cylinders, Cones, and Spheres — Cumulative exam Answers

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm.

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.Which expression represents the volume of the prism, in cubic units?

An oblique prism has a square base and height of 3 centimeters.

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.

The height of a cylinder is 6 inches. The diameter of the circular base of the figure is 10 inches.

An oblique cone has a radius of 5 units and a height of 9 units.

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Circle Y is shown. Chords R T and S U intersect. Arc R S is 106 degrees. The angle that intercepts arc R S is 94 degrees.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm.What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

Which pair of triangles can be proven congruent by the HL theorem?

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.What is the greatest possible whole-number value of the congruent side lengths?

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Which statements about the cylinder are true? Select two options.

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

In the diagram, .

The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem.Which mathematical statement is missing?

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.What is the lateral area of the smaller cylinder?

A regular hexagon is shown.

The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D.

Consider the diagram.