NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 50 of 100

Marks: +1, -0

Each vertical face of square based vertical pillar of height 3 m has 7 equal, semi-cylindrical surfaces in such a way that its horizontal cross-section is as shown in the figure.

If the radius of each semi circle is 10 cm, the volume (in

m^3

) of the pillar so designed (taking

π=22/7

) is

5.88
6.14
6.42
7.2

Validate

Solution:

\text "Area of square"=(7×\;\text"diameter of semicircle"\;)^{2}

=(7×20)^{2}=19600{cm}^{2}

Area of semicircle

=\;\;{π}/{2}(10)^{2}=\;\;{1100}/{7}{cm}^{2}

∴Volume of Pillar = (Area of figure) x height

=300(1900+28×\;\;{1100}/{7})

=300(19600+4400)=300×24000

=7200000cm^3=7.2cm^3

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