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- Question
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
- Correct Answer
- 60 cm
ExplanationRadius of circumcircle of an equilateral triangle = side /?3R = a/?3a = R?3 = 20?3 *?3 = 60cm - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. What is the surface area of the cuboid?
Options- A. 288 sq.cm
- B. 216 sq.cm
- C. 144 sq.cm
- D. Cannot be determined due to insufficient data Discuss
- 8. The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?
Options- A. 572 cub.cm
- B. 728 cub.cm
- C. 1144 cub.cm
- D. None of the above Discuss
- 9. The corners of a square of side ?a? are cut away so as to form a regular octagon. What is the side of the octagon?
Options- A. a(?2 ?1)
- B. a(?3 ?1)
- C. a/?2+2
- D. a/3 Discuss
- 10. Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?
Options- A. Only one
- B. Only two
- C. Only three
- D. Infinitely many Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 6 cm
Explanation:
Perimeter of triangle ABC ? Perimeter of triangle ADC = (9+40+41) - (15+28+41) = 6 cm
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: 14 : 11
Correct Answer: 6?3:1
Correct Answer: 6?3:1
Correct Answer: 20?3 cm
Correct Answer: 288 sq.cm
Explanation:
Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm......(i)
and
?(l^2+b^2+h^2) = 14cm .....(ii)
Surface area of cuboid = 2(lb+bh+lh)
Squaring eq (i) gives
+ 2(lb+bh+lh) = 484
Substituting l^2+b^2+h^2 from eq (i)
2(lb+bh+lh) = 484 -196 = 288 sq.cm
Correct Answer: 1144 cub.cm
Correct Answer: a(?2 ?1)
Correct Answer: Only one
Explanation:
let n-1, n, n+1 be 3 consecutive integers
So
(n+1)^2= n^2+ (n-1)^2
(n+1)^2-(n-1)^2= n^2
4n = n^2
So n = 0 or n = 4
n can?t be 0 as n-1 will be negative then
So 3,4 and 5 is the only triplet formed.
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