These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.

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Geometry and Mensuration: Test 7

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Question 1

A hemispherical bowl is 176 cm round the brim. Supposing it to be half full, how many persons may be served from it in hemispherical glasses 4 cm in diameter at the top?

A

1372

B

1272

C

1172

D

1472

Question 1 Explanation:

Let the radius of the bigger hemisphere is 'r'. We have
2πr = 176 => r = 28 cm Volume of the half hemisphere = ½ x 2/3 x π x 28^{3} = 21952/3 cm^{3} The volume of one hemispherical glass = 2/3 π x 8 = 16 π/3 cm^{3} Hence the number of persons served =(21952 π /3) x (3/16 π) = 1372

Question 2

A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is Rs.100 per m, the area of the farm is 1200 m 2 and the short side is 30 m long. How much would the job cost?

A

Rs.14000

B

Rs.12000

C

Rs.7000

D

Rs.15000

Question 2 Explanation:

Question 3

A lawn is in the form of an isosceles triangle. The cost of turfing it came to Rs.1200 at Rs.4 per m2. If the base be 40 m long, find the length of equal side.

A

25 m

B

24 m

C

26 m

D

None of these

Question 3 Explanation:

Question 4

A landowner increased the length and breadth of a rectangular plot by 10% and 20% respectively. Find the percentage change in the area of the plot.

A

35%

B

33%

C

22.22%

D

None of these

Question 4 Explanation:

New length = 1.1 of the old length New breadth = 1.2 of the old breadth New area = 1.1X1.2 of old area 1.32 of old area. Increase = 32 % Correct option is (d)

Question 5

There are two circles of different radie. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle?

A

12π cm

B

16π cm

C

24π cm

D

32π cm

Question 5 Explanation:

Radius of the larger circle= 2 x √196 = 2x14 = 28cm Radius of the smaller circle=3/7 x 28 = 12cm Circumference=2∏r = 2∏ x 12 = 24∏

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