Geometric Shapes and Their Properties

A polygon is a two-dimensional shape with straight sides. A circle is a two-dimensional shape with no sides.

The sum of the interior angles of a triangle is always 180°.

The area of a square is given by the formula A = s², where s is the length of a side. Therefore, the area of a square with side length 5 cm is 5² = 25 cm².

The volume of a cube is given by the formula V = s³, where s is the length of a side. Therefore, the volume of a cube with side length 4 cm is 4³ = 64 cm³.

The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. Therefore, the surface area of a sphere with radius 6 cm is 4π(6²) = 144π cm².

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base, h is the height of the cylinder, and π is the constant pi (approximately 3.14). Therefore, the volume of a cylinder with radius 5 cm and height 10 cm is π(5²)(10) = 250π cm³.

The surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base, l is the slant height of the cone, and π is the constant pi (approximately 3.14). The slant height of a cone is given by the formula l = √sqrt(r² + h²), where h is the height of the cone. Therefore, the surface area of a cone with radius 4 cm and height 6 cm is π(4)(4 + √sqrt(4² + 6²)) = 100π cm².

The volume of a pyramid with square base is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of a square is given by the formula A = s², where s is the length of a side. Therefore, the volume of a pyramid with square base side length 8 cm and height 12 cm is (1/3)(8²)(12) = 256 cm³.

The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. The radius of a sphere is half of its diameter. Therefore, the radius of a sphere with diameter 10 cm is 5 cm. Therefore, the surface area of a sphere with diameter 10 cm is 4π(5²) = 300π cm².

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base, h is the height of the cylinder, and π is the constant pi (approximately 3.14). Therefore, the volume of a cylinder with radius 7 cm and height 15 cm is π(7²)(15) = 1540π cm³.

The surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base, l is the slant height of the cone, and π is the constant pi (approximately 3.14). The slant height of a cone is given by the formula l = √sqrt(r² + h²), where h is the height of the cone. Therefore, the surface area of a cone with radius 6 cm and height 8 cm is π(6)(6 + √sqrt(6² + 8²)) = 300π cm².

The volume of a pyramid with square base is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of a square is given by the formula A = s², where s is the length of a side. Therefore, the volume of a pyramid with square base side length 10 cm and height 14 cm is (1/3)(10²)(14) = 1120 cm³.

The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. Therefore, the surface area of a sphere with radius 8 cm is 4π(8²) = 256π cm².

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base, h is the height of the cylinder, and π is the constant pi (approximately 3.14). Therefore, the volume of a cylinder with radius 9 cm and height 18 cm is π(9²)(18) = 4536π cm³.