Volume & Surface Area Assessment Test

1) The quantity of three-dimensional space enclosed by a closed surface is called...

Plane

Point

Volume

Space

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.

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.

2) What is the area of a triangle?

Breadth × length

1/2 × breadth × height

1/2 × Height × height

1/2 × Length × length

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.

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.

3) What is the area of a sphere?

Length × height

4 × pi × radius^3

Pi × pi

Pi

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.

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.

4) What is the area of a circle?

Pi × radius^2

Pi

Radius × height

Width × radius

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".

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".

5) What is the area of a rectangle?

Length × volume

Length × breadth

Breadth × pi

Pi × length

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."

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."

6) An example of a three dimensional shape is a...

Square

Line

Circle

Cube

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.

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.

7) What is the volume of a cylinder?

Area × height

Pi × height × weight

Pi × radius^2 × height

Length × height

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.

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.

8) What is the volume of a rectangle?

Length × breadth × height

Length × height

Width × length

Height × breadth × width

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."

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."

9) Area can be measured in which of the following?

Metre square

Cubic metre

Cm

Litres

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.

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.

10) The extent of a two-dimensional figure or shape is called...

Plane

Surface

Area

Volume

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.

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.