Q17 of 34 Page 1

Mathematics teacher of a school took her 10th standard students to show Red fort. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Red fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.


i. How much cloth material will be required to cover 2 big domes each of radius


2.5 metres? (Take

i. Cloth material required = 2 × S A of hemispherical dome


= 2 × 2π r2


= 2 × 2 × × (2.5)2 m2


= 78.57 m2


ii. Volume of a cylindrical pillar = π r2h


iii. Lateral surface area = 2 × 2πrh


= 4 × x 1.4 x 7 m2


= 123.2 m2


iv. Volume of hemisphere = π r3


= (3.5)3 m3


= 89.83 m3


v. Sum of the volumes of two hemispheres of radius 1 cm each


= 2 × π13


Volume of sphere of radius 2cm = 4/3 π 23


So, required ratio = = 1 : 8


More from this chapter

All 34 →
15

A tower stands vertically on the ground. From a point on the ground, which is 15m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°.Find the height of the tower.

 16

Probability of an event E + Probability of the event ̅E (not E) is, _______

 18

Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to sow seeds of flowering plants on the remaining area of the plot.


Considering A as origin, answer question (i) to (v)


i. Considering A as the origin, what are the coordinates of A?


a) (0,1) b) (1,0) c) (0,0) d)(-1,-1)


ii. What are the coordinates of P?


a) (4,6) b)( 6,4) c) (4,5) d) (5,4)


iii. What are the coordinates of R?


a) (6,5) b) (5,6) c) ( 6,0) d) (7,4)


iv. What are the coordinates of D?


a) (16,0) b) (0,0) c) (0,16) d) (16,1)


v. What are the coordinate of P if D is taken as the origin?


a) ( 12,2) b ) (-12,6) c) (12,3) d) (6,10)


 19

Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure.


i. Rahul tied the sticks at what angles to each other?


a) 30° b) 60° c) 90° d) 60°


ii. Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?


a) RHS b) SAS c) SSA d) AAS


iii. Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio,


a) 2:3 b) 4:9 c) 81:16 d) 16:81


iv. In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,


a) Pythagoras theorem b) Thales theorem


c) Converse of Thales theorem d) Converse of Pythagoras theorem


v. What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?


a) 48 cm2 b) 14 cm2 c) 24 cm2 d) 96 cm2