Question Bank  Geometry  Hemant Malhotra

Q20) What is the least possible number of cuts required to cut a cube into 34 identical pieces ?

let number of cuts along length , width and height is a,b,c and total number of cuts=a+b+c
number of cubes =(a+1)(b+1)(c+1)
If product is cnstant sum will be minimum if they are very close to each other
here (a+1)(b+1)(c+1)=1 * 2 * 17
so a+1+b+1+c+1=1+2+17 so a+b+c=17

Q21) A right circular cylindrical vessel having height 20 cm and inner diameter 10 cm is filled with water upto 15 cm of it's height as measured from the base. Find the angle by which the cylinder must be tilted so that the water in the cylinder is just about to fall out?

Q22) The sides of a triangle of area 6 are in AP. If the sides have integer lengths, what is the length of the longest side?

Q23) If in a triangle ABC, AB = BC = 6m and CD = 10cm then what is the difference between the incentre and centroid of the triangle ?

Q24) In an art class the teacher tells the students to draw the largest circle possible on a piece of paper in the shape of a square and then draw a rectangle lying between the circumference of the circle and the edge of the square such that a corner of the rectangle lies on the circumference of the circle and two sides of the rectangle coincide with those of the square. If the rectangle measures 10 cm × 20 cm then what is the area of the sheet of paper?

Q25) A circle circumscribes a regular hexagon H1 and is inscribed inside a regular hexagon H2. What is the ratio of the areas of H1 and H2?

Q26) In a triangle ABC with AB = 14 cm, D and E are points on BC and AC respectively such that BE and AD intersect at point F and the area of ∆ BFD = area of ∆ AFE. Also BD:DC = 2:5. Find the length of DE.

Q27)

Q28) If the sum of lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ?

@hemant_malhotra 1000?

@hemant_malhotra 218?


@hemant_malhotra 1250?

Q29)

Q30) Five equal squares are joined together to form a rectangle whose perimeter is 372. What is the area of one square?

Q31) 3 identical right angle cones with base radius r are placed on their bases so that each is touching the other two.The radius of circle drawn through their vertices is:
a. smaller than r
b. Equal to r
c. larger than r
d. Depends on height

It's like three circles touching each other & when u meet center it will form equilateral triangle with side 2r .. and Radius of circle going through it will be equal to circumradius = 2r/sqrt3 so greater then r

Q32)

Q33)