PYQ Vault

Frustum (bucket, glass, tub): volume, slant height or surface area from end radii and height

This type of question, asked 5 times: CDS 2 2016, CDS 1 2019, CDS 2 2020, CDS 2 2021, CDS 1 2025. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    55
    A drinking glass of height 24 cm is in the shape of frustum of a cone and diameters of its bottom and top circular ends are 4 cm and 18 cm respectively. If we take capacity of the glass as πx cm3\pi x\ \text{cm}^3, then what is the value of xx ?

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2019

    68
    A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are 6 cm and 12 cm respectively. If the height of the bucket is 7 cm, what is the capacity of the bucket ?

    Tap an option to check your answer.

  3. Question 3

    CDS 2 2020

    89
    The radii of the flat circular faces of a bucket are x and 2x. If the height of the bucket is 3x, what is the capacity of the bucket ? (Assume π=227\pi = \frac{22}{7})

    Tap an option to check your answer.

  4. Question 4

    CDS 2 2021

    73
    A tub is in the shape of a frustum of a cone. The radii of two circular ends of the tub are 105 cm and 42 cm. If the vertical height of the tub is 16 cm, what is its slant height ?

    Tap an option to check your answer.

  5. Question 5 (case study, 2 parts)

    CDS 1 2025

    Consider the following for the next two (02) items that follow : A frustum of a right cone has a top of diameter 2k, bottom of diameter 2.5k and height k.
    51
    What is the whole surface area of the frustum ?

    Tap an option to check your answer.

    52
    What is the volume of the frustum ?

    Tap an option to check your answer.