1.
What is the area of a circle?
Correct Answer
A. Pi × radius^2
Explanation
The area of a circle is calculated by multiplying pi (approximately 3.14) by the square of the radius. This formula is derived from the geometric properties of a circle, where the radius is the distance from the center of the circle to any point on its circumference. Squaring the radius ensures that the area is always positive, as the radius can be negative in some cases. Thus, the correct answer is "Pi × radius^2".
2.
What is the volume of a rectangle?
Correct Answer
A. Length × breadth × height
Explanation
The volume of a rectangle is calculated by multiplying its length, breadth, and height. This formula accounts for all three dimensions of the rectangle, resulting in a three-dimensional measurement of space. Therefore, the correct answer is "Length × breadth × height."
3.
An example of a three dimensional shape is a...
Correct Answer
D. Cube
Explanation
A cube is an example of a three-dimensional shape because it has length, width, and height. It is a solid object with six equal square faces.
4.
The quantity of three-dimensional space enclosed by a closed surface is called...
Correct Answer
C. Volume
Explanation
The quantity of three-dimensional space enclosed by a closed surface is called volume. Volume represents the amount of space occupied by an object or a region. It is a measure of capacity and is typically expressed in cubic units.
5.
What is the volume of a cylinder?
Correct Answer
C. Pi × radius^2 × height
Explanation
The correct answer is Pi × radius^2 × height. This formula represents the volume of a cylinder, where Pi is a mathematical constant approximately equal to 3.14, radius is the distance from the center of the circular base to its edge, and height is the distance between the two circular bases. By multiplying the square of the radius by the height and then multiplying it by Pi, we can calculate the volume of the cylinder.
6.
Area can be measured in which of the following?
Correct Answer
A. Metre square
Explanation
Area can be measured in square units, such as square meters. The unit "metre square" represents the measurement of an area, where the length and width of a two-dimensional shape are both measured in meters. Cubic meter, cm, and liters are units used to measure volume or capacity, not area.
7.
The extent of a two-dimensional figure or shape is called...
Correct Answer
C. Area
Explanation
The correct answer is "Area." In mathematics, the area refers to the extent or size of a two-dimensional figure or shape. It is a measurement of the amount of space inside the boundaries of the shape. The area is typically expressed in square units, such as square meters or square inches. It is different from volume, which is the measure of space occupied by a three-dimensional object.
8.
What is the area of a rectangle?
Correct Answer
B. Length × breadth
Explanation
The area of a rectangle is found by multiplying its length and breadth. This is because the area of a rectangle is equal to the product of its two sides. Therefore, the correct answer is "Length × breadth."
9.
What is the area of a triangle?
Correct Answer
B. 1/2 × breadth × height
Explanation
The correct answer is 1/2 × breadth × height. This formula represents the area of a triangle, where the base of the triangle is represented by the breadth and the height of the triangle is represented by the height. To find the area of a triangle, you multiply the breadth by the height and then divide the result by 2. This formula is derived from the fact that the area of a triangle is equal to half the product of its base and height.
10.
What is the area of a sphere?
Correct Answer
B. 4 × pi × radius^3
Explanation
The correct answer is 4 × pi × radius^3. The formula for finding the area of a sphere is 4 times pi times the radius cubed. This formula takes into account the three-dimensional nature of a sphere, where the radius is multiplied by itself twice (cubed) and then multiplied by 4 and pi. This calculation gives the total surface area of the sphere.