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The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint costs 5 paise per cm².

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402. The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

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403. Find the mean of the following marks of 20 students on a screening test, (out of 100) 76, 44, 45, 87, 71, 72, 82, 83, 41, 32, 75, 32, 46, 78, 17, 70, 84, 12, 77, 74

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404. The mean of 10, 12, 16, 20, p and 26 is 17. Find the value of p.

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Long Answer Type

405.

Find the mean of each of the following distributions :

(i)

x_i	10	15	20	25	30	35	40	Total
f_i	4	6	8	18	6	5	3	50

(ii)

x_i	12	13	14	15	16	17	18	Total
f_i	1	3	4	8	10	3	1	30

(iii)

x_i	50	75	100	125	150	175	200	Total
f_i	12	18	50	70	25	15	10	200

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Short Answer Type

406.

The following data have been overanged in ascending order. If the median of these data is 63, then find the value of x : 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

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407.

Find the median of the following data:

95, 65, 75, 70, 75, 100, 50, 40.

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408. The mean of 40 observations was 160. It was detected on rechecking that the value 165 was wrongly copied as 125. Find the correct mean.

∵ Mean of 40 observations = 160
∴ Sum of 40 observations = 160 x 40 = 6400 Corrected sum of 40 observations

= 6400 - 125 + 165
= 6440

$therefore$ Correct mean = $6440 over 40 equals 161$

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409. 2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

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410. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner curved surface area of the vessel.

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