Geometry : Practice Problems

Q.1. The length of the longest rod which can fit into a cubical room of 5 m side is
A. 5.334 m
B. 12.11 m
C. 9.320 m
D. 8.440 m
E. 3.050 m
Q.2. The breadth of a garden is half its length. A playground measuring 45 sq. metre occupies one fourth of the total area of the garden. The length of the garden is
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A. 6m
B. 3m
C. 4m
D. 5m
E. 2m
Q.3. The diagonals of a rhombus are 4m and 3m. What is the length of each side of the rhombus?
A. 2.5m
B. 3.5m
C. 4.5m
D. 5.5m
E. 6.5m
Q.4. One side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then the length of the other diagonal is
A. 2cm
B. 16cm
C. 18cm
D. 20cm
E. 12cm
Q.5. The measure of an angle which is five times its complement is
A. 26°
B. 75°
C. 78°
D. 18°
E. 122°
Q.6. The base of a prism is a triangle of sides 6, 8 and 10 m respectively. The height of the prism is 20 m. Find its volume.
A. 240 m3
B. 480 m3
C. 420 m3
D. 315 m3
E. 150 m3
Q.7. If the breadth of a rectangle is decreased by 20 % and the length increased by 10 %, a square of area 1936 m2 is obtained. The area of the rectangle in square metres is
A. 2200
B. 3500
C. 2250
D. 1450
E. 4506
Q8. What is the arc length that is intercepted by an inscribed angle of 42o on a circle with radius 24?
A. 70.4
B. 325.2
C. 324
D. 7.6
E. 233.2
Q9. The height of a cylinder is 16 cm and the radius of the base is 6 cm. Find the area of the curved surface of the cylinder.
A. 480 sqcm
B. 560 sqcm
C. 603 sqcm
D. 720 sqcm0
E. 800 sqcm
Q10. A swimming bath is 240 m long and 12.5 m wide. How many litres must be pumped into it to raise the water-level by 1 cm?
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A. 3,000 litres
B. 300,000 litres
C. 30,000 litres
D. 3,000,000 litres
E. 300 litres