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401.
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.

For a wooden sphere
Diameter = 21 cm

$therefore$ Radius (r) = $21 over 2 space cm$

∴ Surface area of a wooden sphere = 4

$therefore space space straight r squared space equals 4 cross times 22 over 7 cross times open parentheses 21 over 2 close parentheses squared equals 1386 space cm squared$
∴ Surface area of a wooden sphere to be painted = 1386 – $straight pi$ (1.5)²

$equals 1386 minus 22 over 7 left parenthesis 1.5 right parenthesis squared equals 1378.93$
∴ Surface area of eight wooden spheres = 1378.93 x 8 = 11031.44 cm² Cost of painting silver @ 25 paise per cm² = 11031.44 x 25 paise

$equals straight र fraction numerator 11031.44 cross times 25 over denominator 100 end fraction equals straight र space 2757.86$

For a cylindrical support
Radius (r) = 1.5 cm Height (h) = 7 cm
Surface area of a cylindrical support = 2 $straight pi$ rh

$equals 2 cross times 22 over 7 cross times 1.5 cross times 7 equals 66 space cm squared$

∴ Surface area of eight cylindrical supports = 66 x 8 = 528 cm²∴ Cost of painting black @ 5 paise per cm² = 528 x 5 paise

$equals straight र space fraction numerator 528 cross times 5 over denominator 100 end fraction equals bold र bold space bold space bold 26 bold. bold 40$

∴ Cost of paint required = 2757.86 + 26.40 = र 2784.26 (approx.)

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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.

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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.

2531 Views

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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