Pythagoras Area Volume

What is the length of the hypotenuse of a right triangle with legs of length 9 and 12?

15

What is the length of the other leg of a right triangle with a hypotenuse of length 20 and one leg of length 16?

12

Which set of side lengths forms a right triangle: 6, 8, 10 or 7, 9, 11?

6, 8, 10

What is the distance between the points (1, 2) and (4, 6)?

5

What is the length of the diagonal of a rectangular box with dimensions 4, 3, and 12?

13

What is the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 7?

7√2

What is the length of the hypotenuse of a 30°-60°-90° triangle with a short leg of length 5?

10

If a 26-foot ladder leans against a wall with its base 10 feet from the wall, how many feet up the wall does the ladder reach?

24

What is the surface area of a rectangular prism with length 6, width 5, and height 4?

148

What is the surface area of a cube with an edge length of 8 cm?

384

What is the surface area of a cylinder with radius 4 and height 6, in terms of pi?

80π

If a cube has a volume of 216 cubic units, what is the edge length of the cube?

6

What is the volume of a rectangular prism with length 9, width 4, and height 5?

180

What is the volume of a cylinder with radius 3 and height 11, in terms of pi?

99π

What is the volume of a cone with radius 6 and height 10, in terms of pi?

120π

What is the volume of a sphere with radius 3, in terms of pi?

36π

What is the volume of a triangular prism with a right-triangle cross-section of legs 6 and 8, and a prism length of 15 units?

360

What is the volume of a square pyramid with a base edge of 10 and a height of 12?

400

If a cylinder and a cone have the same radius and height, and the cylinder's volume is 150 cubic units, what is the cone's volume?

50

What is the length of the diagonal connecting opposite corners of a rectangular box with dimensions 4 by 4 by 7?

9

What is the length of the hypotenuse of a right triangle with legs of length 8 and 15?

17

What is the length of the other leg of a right triangle with a hypotenuse of length 17 and one leg of length 8?

15

Which set of side lengths forms a right triangle: 5, 12, 13 or 6, 7, 8?

5, 12, 13

What is the distance between the points (-2, 1) and (3, 13)?

13

What is the length of the diagonal of a rectangular box with dimensions 8, 6, and 24?

26

What is the length of each leg of a 45°-45°-90° triangle with a hypotenuse of length 10√2?

10

What is the length of the short leg of a 30°-60°-90° triangle with a hypotenuse of length 18?

9

If a wire is stretched from the top of a 30-foot pole to a point on the ground 40 feet from the base of the pole, what is the length of the wire?

50

What is the surface area of a rectangular prism with length 10, width 7, and height 3?

242

What is the surface area of a cube with an edge length of 11?

726

What is the surface area of a cylinder with radius 5 and height 8, in terms of pi?

130π

If a sphere has a surface area of 196π, what is its radius?

7

What is the volume of a rectangular prism with length 12, width 5, and height 3?

180

What is the volume of a cylinder with radius 6 and height 5, in terms of pi?

180π

What is the volume of a cone with radius 9 and height 4, in terms of pi?

108π

What is the volume of a sphere with radius 6, in terms of pi?

288π

What is the volume of a triangular prism with a right-triangle cross-section of legs 9 and 12, and a length of 10 units?

540

What is the volume of a square pyramid with a base edge of 8 and a height of 15?

320

If a cylinder and a cone have the same radius and height, and the cone's volume is 40 cubic units, what is the cylinder's volume?

120

What is the length of the diagonal connecting opposite corners of a rectangular box with dimensions 6 by 6 by 7?

11

What is the Pythagorean theorem formula relating legs a and b to hypotenuse c?

a

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

√((x2 - x1)

What is the formula for the surface area of a rectangular prism with length l, width w, and height h?

2lw + 2lh + 2wh

What is the formula for the surface area of a cube with edge length s?

6s

What is the formula for the total surface area of a cylinder with radius r and height h?

2πr

What is the formula for the volume of a cylinder with radius r and height h?

πr

What is the formula for the volume of a cone with radius r and height h?

(1/3)πr

What is the formula for the volume of a sphere with radius r?

(4/3)πr

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

4πr

What is the formula for the volume of a pyramid with base area B and height h?

(1/3)Bh