CBSE Class 9 Math: Ten Important Questions

CBSE Class 9 Math: Ten Important Questions

1. ABCD is a rhombus and P, Q, R, S are mid-points of AB, BC, CD and DA Prove that quadrilateral PQRS is a rectangle.

2. ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

3. Recall that two circles are congruent if they have the same Prove that equal chords of congruent circles subtend equal angles at their centres.

4. A conical tent is 10 m high and the radius of its base is 24m.

Find:

i. Slant height of the tent.

ii. Cost of the canvas required to make the tent, if the cost of one m² canvas is Rs. 70.

5. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm.  (Use pi = 14)

6. A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

7. Prove that the parallelogram which is a rectangle has the greatest area.

8. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm by 20 cm by 5 cm and the smaller of dimensions 15 cm by 12 cm by 5 cm. 5% of the total surface area is required extra, for all the overlaps. If the cost of the card board is Rs. 4 for 1000 cm², find the cost of cardboard required for supplying 250 boxes of each kind.

9. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet.

a. Determine:

i. The area of the sheet required for making the

ii. The cost of sheet for it, if a sheet measuring 1m² cost 20.

b. Find:

i. The lateral or curved surface area of a petrol storage tank that is 4.2 m in diameter and 4.5 m high.

ii. How much steel was actually used if 1/12 of the steel actually used was wasted in making the tank?