What is the formula for the area of a rectangle?

The area of a rectangle is calculated using the formula A = length × width. For example, if the length is 5 units and the width is 3 units, the area is 5 × 3 = 15 square units.

How do you find the circumference of a circle?

The circumference of a circle is found using the formula C = 2πr, where r is the radius. For example, if the radius is 4 units, the circumference is C = 2 × π × 4 = 8π units.

What is the volume of a cylinder?

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. For example, if the radius is 3 units and the height is 5 units, the volume is V = π × (3)² × 5 = 45π cubic units.

If the length of a side of a square is doubled, how does the area change?

If the length of a side of a square is doubled, the area increases by a factor of four. The area of a square is A = side². If the original side is s, the new area becomes (2s)² = 4s², which is four times the original area.

A triangle has a base of 10 units and a height of 6 units. What is its area?

The area of a triangle is calculated using the formula A = ½ × base × height. For this triangle, the area is A = ½ × 10 × 6 = 30 square units.

What is the formula for the volume of a sphere?

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius. For example, if the radius is 3 units, the volume is V = (4/3) × π × (3)³ = 36π cubic units.

How do you calculate the surface area of a cube?

The surface area of a cube is calculated using the formula SA = 6a², where a is the length of a side. For example, if a = 2 units, the surface area is SA = 6 × (2)² = 24 square units.

What is the formula for the area of a trapezium?

The area of a trapezium is calculated using the formula A = ½ × (base1 + base2) × height. For example, if base1 = 6 units, base2 = 4 units, and height = 5 units, the area is A = ½ × (6 + 4) × 5 = 25 square units.

A cone has a radius of 3 units and a height of 4 units. What is its volume?

The volume of a cone is calculated using the formula V = (1/3)πr²h. For this cone, the volume is V = (1/3) × π × (3)² × 4 = 12π cubic units.

What is the formula for the perimeter of a rectangle?

The perimeter of a rectangle is calculated using the formula P = 2(length + width). For example, if the length is 5 units and the width is 3 units, the perimeter is P = 2(5 + 3) = 16 units.

If the height of a cylinder is tripled while the radius remains constant, how does the volume change?

The volume of a cylinder is given by V = πr²h. If the height is tripled, the new volume becomes V = πr²(3h) = 3πr²h, which means the volume also triples.

A circle has a diameter of 10 units. What is its area?

The area of a circle is calculated using A = πr². The radius r is half of the diameter, so r = 10/2 = 5 units. Therefore, the area is A = π(5)² = 25π square units.