mensuration Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Question :1

Water is filled in a container in such a manner that its volume doubles every 5 minutes. If it takes 30 minutes for the container to be full, in how much time will it be one– fourth full?

Answer: (a)

At sometimes, the container was full.

At 25 minutes, it was holy full.

At 20 minutes, it was the fourth full.

So, option (c) is correct.

Question :2

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?

Answer: (d)

Perimeter of the circle = 2 π r = 2(18 + 26)

⇒2 × ${22}/7$ × r = 88⇒r = 14

∴ Area of the circle

=π $r^2 = {22}/{7} × 14 × 14 = 616 cm^2$.

Question :3

A field is 125 m long and 15 m wide. A tank 10m × 7.5m × 6m was dug in it and the Earth thus dug out was spread equally on the remaining field. The level of the field thus raised is equal to which one of the following?

Answer: (a)

Area of tank, BCDE = 10 × 7.5 = 75 $m^2$

mensuration-area-and-volume-aptitude-mcq

Area of remaining field ABEDFGA

= 125 × 15 – 75 = 1800 sq m

Volume of Earth dug = 10 ×7.5 × 6 = 450 cu m

By given condition, 1800 × h = 450

⇒ h = $1/4 m = 1/4 × 100$ cm = 25 cm

Question :4

What is the volume of a cone of maximum volume cut out from a cube of edge 2a such that their bases are on the same plane?

Answer: (a)

edge of cube = 2a

radius of cone = ${2a}/2$ = a

hight of cone = 2a

Volume of cone = $1/3 π r^2 h = 1/3 × π × a^2 × 2a$

= ${2a^3 π}/3 = {2πa^3}/3$

Question :5

If x and y are respectively the areas of a square and a rhombus of sides of same length, then what is x : y?

Answer: (b)

As we know that, if the length of square and rhombus are same, then the area should be same

∴ x : y = 1 : 1

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