Test: Geometry & Mensuration (2019-2010) - UPSC MCQ

Number of cubes have only one face painted

= 2 × 4 + 2 × 1
= 8 + 2 = 10

For easily count the number of triangles in the given three-dimensional figure, devide the given figure into three parts-top, bottom and middle.
In each of the top and bottom part, there are 5 triangles which are based on a pentagon. In middle part, there are 5 quadrilaterals inclosed between two pentagons.
Further each quadrilateral is divided into two triangles.
Hence in the middle part, there are 10 triangles.
∴ Total number of triangles in the given 3D-figure.
= (No. of triangles in top part) + (No. of triangle in bottom part) + (No. of triangle in middle part)
= 5+ 5 + 10 = 20

Diagonal of rectangle = 5 cm

then velue of l and b must be 4 and 3
Area of ractangle = 4 × 3 = 12 cm²
Area of square be a²
12 × a² = 12
∴ a² = 1 sq. cm.

Area of rectangle = 12 × 8 cm² = 96 cm²
Rectangle is used to construct a closed cube.
Surface area of cube formed = Area of given rectangle.
6 (side)² = 96 cm²
⇒ side =  ⇒ side = 4 cm.

Volume of cylindrical over head tank = πr²h 

Volume of underground tank = (5.5 × 4 × 6)m³ = 132m³
Portion of underground tank still filled with water after filling the overhead tank completely.

From above diagram, it is clear that Y, V and W are parallel.

Let initial dimensions be, l & b
∴ Final length is 1.4 l
Final breadth is 0.8 b
∴ Final area is = 1.4 l × 0.8 b
= 1.12 lb
∴ Area is increased by 12%.
Shortcut Method : + 40 – 20 + 
= 20 – 8 = 12%
Therefore, the area of the new garden increased by 12%.

Milk in 1st Glass = (1/2)V
Milk in 2nd Glass = (3/4)V
Now the 1st glass = (1/2)V
Now the 2nd glass = (1/4)V
When both glasses are mixed then the ratio of milk to water

Volume of tank = 20 x 15 x 6 m³ 
= 20 x 15 x 6 x 1000 litre
∴ The water of the tank will last for

i.e. The water of the tank will last for 3 days.

Perimeter of bigger coin : Perimeter of smaller coin
= 2π(3) : 2π(1) = 3 : 1
Hence, smaller coin will roll 3 times around the bigger coin.