Cavalieri's Principle and Volume of Composite Figures — Cumulative exam Answers

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

Circle K is shown. Tangents S T and U T intersect at point T outside of the circle. A line is drawn from point T to point R on the opposite side of the circle. It goes through center point K. Lines are drawn from points S and U to center point K.

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

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.

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase.He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.

Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Rhombus LMNO is shown with its diagonals.

Maggie puts together two isosceles triangles so that they share a base, creating a kite. Each leg of the upper triangle measures 41 inches and each leg of the lower one measures 50 inches.

Triangle Q R S is shown. Angle Q R S is a right angle. Angle R S Q is 30 degrees and angle S Q R is 60 degrees. The length of R S is 5 StartRoot 3 EndRoot, the length of S Q is 10, and the length of R Q is 5.

Angle G is a circumscribed angle of circle E.

What is the radius of a circle whose equation is (x – 7)2 + (y – 10)2 = 4?

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Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD.

The radius of the sphere is 10 units.

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°.Law of cosines: a2 = b2 + c2 – 2bccos(A)

Which is the equation of an asymptote of the hyperbola whose equation is = 1?