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- Question
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What is the ratio of the volume of the sphere to that of cone?
Options- A. 6?3:1
- B. 7 : 2
- C. 3?3:1
- D. 5?3:1
- Correct Answer
- 6?3:1
- 1. A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What is the ratio of the volume of the sphere to that of cone?
Options- A. 6?3:1
- B. 7 : 2
- C. 3?3:1
- D. 5?3:1 Discuss
- 2. ?PQR has sides PQ and PR measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?
Options- A. 1876
- B. 90
- C. 1785
- D. 1786 Discuss
- 3. If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?
Options- A. 20
- B. 36.25
- C. 56.25
- D. 65 Discuss
- 4. In a triangle ABC, AD is angle bisector of ?A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?
Options- A. 150
- B. 200
- C. 210
- D. 240 Discuss
- 5. ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ?BPC?
Options- A. 90
- B. 120
- C. 135
- D. 145 Discuss
- 6. A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What is the ratio of the volume of the cube to that of the cylinder ?
Options- A. 4 : 3
- B. 21 : 16
- C. 14 : 11
- D. 45 : 32 Discuss
- 7. 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 quadrilateral ABCD?
Options- A. 300 SQ.CM
- B. 306 SQ.CM
- C. 312 SQ.CM
- D. 316 SQ.CM Discuss
- 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 difference between perimeter of triangle ABC and perimeter of triangle ADC?
Options- A. 4 cm
- B. 5 cm
- C. 6 cm
- D. 7 cm Discuss
- 9. An equilateral triangle ABC is inscribed in a circle of radius 20?3. What is the length of the side of the triangle?
Options- A. 30 cm
- B. 40 cm
- C. 50 cm
- D. 60 cm Discuss
- 10. An equilateral triangle ABC is inscribed in a circle of radius 20?3. The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?
Options- A. 15 cm
- B. 20 cm
- C. 20?3 cm
- D. 30?3 cm Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 6?3:1
Correct Answer: 1785
Correct Answer: 56.25
Correct Answer: 150
Correct Answer: 120
Correct Answer: 14 : 11
Correct Answer: 316 SQ.CM
Explanation:
Area of quadrilateral ABCD = area of triangle ADC + area of triangle ABC
= 126 + ½ * 9 * 40 = 306
Correct Answer: 6 cm
Explanation:
Perimeter of triangle ABC ? Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm
Correct Answer: 60 cm
Explanation:
Radius of circumcircle of an equilateral triangle = side /?3
R = a/?3
a = R?3 = 20?3 *?3 = 60cm
Correct Answer: 20?3 cm
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