Question

15. Metal spheres, each radius 2cm, are packed in a rectangular box of internal

dimensions 16cm × 8cm × 8cm. When 16 spheres are packed, the box filled with

preservative liquid. Find the volume of liquid.

16. If the lateral surface of a cylinder is 94.2 sq.cm and its height is 5 cm, then find

radius of its base.

17. The surface area of a cuboid is 1372 sq. cm. If its dimensions are in the ratio of

4: 2: 1, then find its length.

18. The radius of a spherical balloon increases from 7 cm to 14 cm when air is being

pumped into it. Find the ratio of surface area of the balloon in the two cases.

19. Find the total surface area of a hemisphere of radius 7 units.

20. The slant height of a cone is 26 cm and base diameter is 20 cm. Find its height.

21. Find the Median of first 10 odd natural numbers

22. The mean of 20, 25, x, 35, 40 is 30. What is the value of x?

23. The data has been arranged in ascending order: 14, 19, 25, 29, x, 39, 41, 48, 54. If the

median of the data is 35. Find x.

24. The mean of 200 observations is 60. If one of the observation which was 100 is

replaced by 300 then what will be the resulting mean?

25. The width of each of five continuous classes in a frequency distribution is 5 and the

lower class limit of the lowest class is 10. What is the upper class limit of the highest

class?

26. If a line segment joining mid-points of two chords of a circle passes through the

centre of the circle, prove that the two chords are parallel.

27. On a common hypotenuse AB, two right angled triangles, ACB and ADB are situated

on opposite sides. Prove that ∠BAC = ∠BDC.

28. If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

29. If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at

P and Q, prove that arc PXA = arc PYB.

30. AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC

passes through the centre of the ​

Answer 1

Step-by-step explanation:

15.

volume of a cuboidal box =L × B × H

= 16 × 8 × 8

= 1024 cubic centimetre v

volume of sphere=4/3.πrcubic.

= 4/3 × 3.14 × 2 × 2 × 2 cubic centimetre

=> 33.4 9 cubic centimetre

volume of 16 spheres= 16 × 33.49. = 535.84 cubic centimetre

NOW,

volume of liquid = volume of box – volume of spheres

=> ( 1024 – 53 5.84)

=> 488.16 cubic centimetres

16.

where, π = 3.14

Radius =' r '.cm

Height = 5 cm

solution...

94.2 = (2πrh)

R = 94.2

____

2πh

94.2

R = ________........

2× 3.14 × 5

94.2

= _____

31.4

=> r = 3 cm.