Volume Using Calculus Assessment Test

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Volume Using Calculus Assessment Test - Quiz

Take our intelligent assessment test to evaluate your knowledge of how we can use calculus and integrals to find volumes like areas and lengths.


Questions and Answers
  • 1. 

     An integral over a 3-dimensional domain is referred to as?

    • A.

      Slope

    • B.

      Volume integral

    • C.

      Space

    • D.

      Function

    Correct Answer
    B. Volume integral
    Explanation
    A volume integral refers to an integral over a 3-dimensional domain. It is used to calculate the total volume of a region in space. By integrating a function over the domain, the volume integral takes into account the contribution of each infinitesimally small volume element within the region, resulting in the total volume. Therefore, the correct answer is volume integral.

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  • 2. 

    The amount of space taken up by a three-dimensional object is?

    • A.

      Volume

    • B.

      Time

    • C.

      Length

    • D.

      Option

    Correct Answer
    A. Volume
    Explanation
    The amount of space taken up by a three-dimensional object is called its volume. Volume is a measurement of the total amount of space that an object occupies in three dimensions - length, width, and height. It is commonly expressed in cubic units such as cubic meters or cubic centimeters. The volume of an object helps us understand its capacity or how much it can hold.

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  • 3. 

    How do you find the volume of a solid?

    • A.

      Length×length

    • B.

      Length×width×height

    • C.

      Breadth×height

    • D.

      Length×height

    Correct Answer
    B. Length×width×height
    Explanation
    To find the volume of a solid, you need to multiply its length, width, and height together. This is because volume is a measure of the amount of space occupied by an object in three dimensions. By multiplying these three dimensions, you can determine the total amount of space the solid occupies. Therefore, the correct answer is length × width × height.

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  • 4. 

    The quantity of three-dimensional space enclosed by a closed surface is?

    • A.

      Term

    • B.

      Vacuum

    • C.

      Volume

    • D.

      Area

    Correct Answer
    C. Volume
    Explanation
    The quantity of three-dimensional space enclosed by a closed surface is referred to as volume. Volume is a measure of the amount of space occupied by an object or a region in three-dimensional space. It is typically measured in cubic units, such as cubic meters or cubic feet. In the context of this question, the correct answer is volume because it directly relates to the quantity of three-dimensional space enclosed by a closed surface.

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  • 5. 

     What is the unit of volume?

    • A.

      Time

    • B.

      Second

    • C.

      Cubic metre

    • D.

      Metre

    Correct Answer
    C. Cubic metre
    Explanation
    The unit of volume is cubic metre. Volume is a measure of the amount of space occupied by an object or substance, and it is typically measured in three dimensions - length, width, and height. The cubic metre is the SI unit for volume and represents the volume of a cube with sides of one metre in length. It is commonly used in scientific and engineering calculations to measure the capacity or size of objects or spaces.

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  • 6. 

    The amount that something can hold is termed?

    • A.

      Figure

    • B.

      Capacity

    • C.

      Power

    • D.

      Number

    Correct Answer
    B. Capacity
    Explanation
    Capacity refers to the amount that something can hold. It is a measure of the maximum volume or quantity that an object, container, or space can accommodate. In this context, the term "capacity" is the most appropriate answer as it directly relates to the amount that something can hold.

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  • 7. 

    Which is an important parameter in calculating the volume of an object with density?

    • A.

      Mass

    • B.

      Time

    • C.

      Height

    • D.

      Figure

    Correct Answer
    A. Mass
    Explanation
    Mass is an important parameter in calculating the volume of an object with density because density is defined as the mass of an object divided by its volume. In order to calculate the volume, we need to know the mass of the object. Therefore, mass is a crucial factor in determining the volume of an object with density.

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  • 8. 

    Which is an important parameter in finding the volume of a pyramid?

    • A.

      Level

    • B.

      Height

    • C.

      Time

    • D.

      Space

    Correct Answer
    B. Height
    Explanation
    The height of a pyramid is an important parameter in finding its volume. The volume of a pyramid is calculated by multiplying the area of its base by its height and dividing it by 3. Without knowing the height, it would not be possible to accurately calculate the volume of the pyramid. Therefore, height is a crucial factor in determining the volume of a pyramid.

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  • 9. 

     How do you find the volume of a triangular pyramid?

    • A.

      1/3AH

    • B.

      1/2B

    • C.

      3AB

    • D.

      2BC

    Correct Answer
    A. 1/3AH
    Explanation
    To find the volume of a triangular pyramid, you can use the formula 1/3 times the area of the base (A) multiplied by the height (H). This is because a triangular pyramid has a base that is a triangle, and the volume is calculated by taking one-third of the product of the base area and the height. Therefore, the correct answer is 1/3AH.

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  • 10. 

    How do you calculate the volume of a cylinder?

    • A.

      πr

    • B.

      πr2

    • C.

      πr^2

    • D.

      πr2h

    Correct Answer
    D. πr2h
    Explanation
    To calculate the volume of a cylinder, you need to multiply the area of the base (which is a circle) by the height of the cylinder. The formula for the area of a circle is πr^2, where r is the radius of the circle. Therefore, the correct formula to calculate the volume of a cylinder is πr^2h, where r is the radius of the base and h is the height of the cylinder.

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