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You are estimating the height of a semicircular arch. Exactly 1 foot from the base of the arch, the arch is 5 feet tall. What is the height of the arch at the center?
A square with 4 cm sides is drawn so that its right edge is tangent to a circle, and the circle passes through two of its vertices. What is the diameter of the circle?
Chord AB on circle C of radius 3 intersects a diameter at X. If AX = 3 and BX = 2, find the length of CX. Express your answer in simplest radical form.
Trapezoid ABCD has base lengths AB = 30 and CD = 54 cm, with congruent 56 cm diagonals. Find the area of triangle ABX. Express your answer in simplest radical form.
Circle A has a radius of 28 inches, and circle B has a 44-inch radius. The distance between their centers is 90 inches. What is the length of segment CD, which is tangent to both circles?
What is the length of the angle bisector to the short leg of a 9-12-15 right triangle? Express your answer in simplest radical form.
The legs of a right triangle are in the ratio 1:2. The angle bisector to the short leg divides it into two segments, one of which is 1 cm longer than the other. Express the perimeter of the triangle in simplest radical form.
The area of a triangle with side lengths 13, 20, and 21 is 126 units square. What would be the area of a triangle with side lengths of 130, 200, and 210?
A small statue is an exact replica of the statues at Easter Island and is just 2 feet tall. The real statues are 14 feet tall and weigh 27,440 pounds. If the stone replica is made of the same stone as the real statues, how many pounds does it weigh?
The surface area of a solid clay hemisphere is 10 cm square. A larger solid clay hemisphere has a surface area of 40 cm square. If the larger hemisphere weighs 2 pounds, how many pounds does the smaller one weigh?
Similar pyramids have altitudes of 3 cm and 4 cm. The volume of the smaller pyramid is 30 cm cube. What is the volume of the larger pyramid?
A cube has a volume of 3 cm cube. The cube is enlarged until its surface area is 100 times the surface area of the original cube. What is the volume of the enlarged cube?
Kaitlyn is making a snowman with three large balls of snow. She rolls three snowballs so that top has a 2-foot diameter, the middle has a 3-foot diameter, and the bottom has a 4-foot diameter. If the weight of the top ball is 80 pounds, what is the weight of the entire snowman?