Mensuration

The volume of a cylinder is calculated using the formula πr²h, where π is approximately 3.14, r is the radius of the cylinder, and h is the height of the cylinder. In this case, we have π x 5² x 10 = 3.14 x 25 x 10 = 785 cm³, which is approximately 314 cm³.

The area of a circle is given by the formula A = πr^2. Substituting r = 5 into the formula, we get A = π(5)^2 = 25π square inches.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Substituting the given value, we get V = (4/3)π * (5 cm)^3 = 250π cm^3.

The area of a circle with radius 10 units is $$A = \frac{1}{2}\pi r^2 = \frac{1}{2}\pi (10)^2 = 100\pi$$. Therefore, the area of the circle is 100\pi square units.

The volume of a sphere with radius 10 units is $$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (10)^3 = 4000\pi$$. Therefore, the volume of the sphere is 4000\pi cubic units.

The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, r = 7 cm, so A = π(7)^2 = 154 cm^2.

The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, A = 1256 cm^2, so πr^2 = 1256. Dividing both sides by π, we get r^2 = 1256 / π ≈ 400. Taking the square root of both sides, we get r ≈ 20 cm.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, C = 56.52 cm, so 2πr = 56.52. Dividing both sides by 2π, we get r = 56.52 / 2π ≈ 9 cm. Therefore, the area of the circle is given by the formula A = πr^2 = π(9)^2 ≈ 274.87 cm^2.

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 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 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.