Challenge your understanding of mensuration with questions on area, volume, and surface calculation concepts. This quiz covers key formulas and methods for solving problems involving shapes like circles, rectangles, cylinders, and cones to strengthen your geometry fundamentals.
What is the formula to find the area of a rectangle with length 12 cm and width 8 cm?
Explanation: The correct formula to calculate the area of a rectangle is length multiplied by width. The other options either represent the perimeter formula (2 × (length + width)), half the area (0.5 × length × width), or are incorrect operations like division (length ÷ width). Only multiplication accurately measures the surface inside the rectangle.
If a cube has a side length of 5 meters, what is the volume of the cube?
Explanation: Volume of a cube is found by raising the side length to the third power: 5 × 5 × 5 equals 125 cubic meters. The option 25 cubic meters is only side squared, 20 is just 4 times the side, and 100 is side squared times two, none of which represent the correct formula for a cube's volume.
Which formula gives the area of a circle with radius 7 centimeters?
Explanation: Area = π × r² is the standard formula for the area of a circle. The option 2 × π × r gives the circumference, π × d also finds the circumference using diameter, and 2 × π × r² is not a standard geometric formula. Only π × r² accurately calculates the surface inside the circle.
The total surface area of a closed cylinder with radius 3 cm and height 10 cm is given by which formula?
Explanation: The total surface area of a closed cylinder is 2πr(r + h), accounting for both circular bases and the lateral area. πr²h gives the volume, 2πrh covers only the curved surface, and πr² + 2πrh adds one base instead of two. Only 2πr(r + h) includes all surfaces of a closed cylinder.
Given a triangle with base 6 cm and height 4 cm, what area formula should be used?
Explanation: Area = 0.5 × base × height is the calculation for a triangle's area using base and height. Multiplying base and height alone gives the area of a rectangle, adding them is not a valid area formula, and 2 × (base + height) is relevant only for perimeter-style measurements.
What is the formula for the volume of a sphere with radius 9 cm?
Explanation: The correct formula for a sphere's volume is (4⁄3)πr³. The formula πr²h gives the volume of a cylinder, 2πrh is for a cylinder's surface area, and πr³ is missing essential coefficients needed for the sphere's volume. Only (4⁄3)πr³ yields the right calculation for a sphere.
If each side of a square is 11 cm, what is the perimeter of the square?
Explanation: A square's perimeter equals four times the side length, so 11 × 4 = 44 cm is correct. 22 cm would only be twice the side, 121 cm is the area (side squared), and 33 cm multiplies the side by three. The only accurate perimeter calculation here is 44 cm.
How do you find the total surface area of a cube with 4 cm edges?
Explanation: The surface area of a cube is 6 times the square of a side since it has 6 equal faces. 4 × side calculates the perimeter of one face, side³ gives the volume, and 2 × (side)² accounts for only two faces. Only multiplying 6 by the side squared covers all faces.
A box has a length of 8 cm, width of 3 cm, and height of 2 cm. What is its volume?
Explanation: The volume of a rectangular prism (box) is found by multiplying length × width × height, so 8 × 3 × 2 = 48 cubic centimeters. 24 and 32 are incorrect arrangements of multiplication, and 13 is unrelated. Only 48 cubic centimeters uses the correct multiplication of all dimensions.
The curved (lateral) surface area of a cone with a slant height of 10 cm and base radius of 5 cm is calculated using which formula?
Explanation: For a cone, the curved surface area formula is πrl, where r is base radius and l is slant height. πr² is area of the base only, 2πrh applies to cylinders, and πr(r + l) adds the base unnecessarily. Only πrl gives the correct curved surface area for a cone.