Volume and Surface Area problems
- 1. The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :
Options- A. 4:7
- B. 7:4
- C. 28:27
- D. 27:28 Also asked in: Bank Exams
Correct Answer: 27:28
- 2. A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take ? = 22/7)
Options- A. 6.67 cm
- B. 5.56 cm
- C. 6.94 cm
- D. 4.63 cm Also asked in: AIEEE, Bank Exams, CAT
Correct Answer: 4.63 cm
- 3. Three consecutive angles of a cycle quadrilateral are in the ratio of 1 : 4 : 5 . The measure of fourth angle is
Options- A. 120°
- B. 60°
- C. 30°
- D. 80° Also asked in: Bank Exams
Correct Answer: 60°
- 4. In triangle ABC, ?ABC = 15 deg. D is a point on BC such that AD = BD. What is the measure of ?ADC (in degrees)?
Options- A. 15
- B. 30
- C. 45
- D. 60 Also asked in: Bank Exams
Correct Answer: 30
- 5. The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?
Options- A. 7/2
- B. 7
- C. 7?2
- D. 14 Also asked in: Bank Exams
Correct Answer: 7
- 6. A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?
Options- A. 77
- B. 154
- C. 87
- D. 38.5 Also asked in: Bank Exams
Correct Answer: 77
- 7. In ?PQR, ?QPR = 45° and the bisectors of ?PQR and ?PRQ meets at O. What is the value (in degrees) of ?QOR?
Options- A. 107.5
- B. 112.5
- C. 117.5
- D. 122.5 Also asked in: Bank Exams
Correct Answer: 112.5
- 8. ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right ?angel. What is the area of triangle ADC?
Options- A. 126 SQ.CM
- B. 124 SQ.CM
- C. 122 SQ.CM
- D. 120 SQ.CM Also asked in: Bank Exams
Correct Answer: 126 SQ.CM
- 9. In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?
Options- A. 2?6 cm
- B. 3?6 cm
- C. 3?7 cm
- D. 6?7 cm Also asked in: Bank Exams
Correct Answer: 6?7 cm
- 10. Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2 Also asked in: Bank Exams
Correct Answer: Both 1 and 2
Explanation:
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ?ABD, AD is a median
?
AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
?
AB + BC + AC > AD + BE +CF
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
third side]
----
1
In triangle ADC,
AC + DC > AD [because, the sum of any two
sides of a tri
angle is always greater than the
third side]
----
2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
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