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- Question
- How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material?
Options- A. 8
- B. 6
- C. 5
- D. 2
- Correct Answer
- 5
ExplanationArea of square plate = (Side)2
= (2d)2
= 4d2
Area of circular plate = ? (d/2)2
= ?d2/4
? Number of square plates
= [(4d2)/4] / [(?d2)/4]
= (4 x 4)/?
? 5
Since, nearest integer value is 5. - 1. The area of rectangle is 1.8 times the area of a square. The length of the rectangle is 5 times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle?
Options- A. 145 cm
- B. 144 cm
- C. 133 cm
- D. 135 cm Discuss
- 2. The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.
Options- A. 30 cm
- B. 40 cm
- C. 21 cm
- D. 45 cm Discuss
- 3. The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?
Options- A. 21 cm
- B. 42?3 cm
- C. 21?3 cm
- D. 42 cm Discuss
- 4. If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct?
Options- A. y4 = 432 x2
- B. y4 = 216 x2
- C. y2 = 432 x2
- D. None of these Discuss
- 5. A square, a circle and equilateral triangle have same perimeter.
Consider the following statements.
I. The area of square is greater than the area of the triangle.
II. The area of circle is less then the area of triangle.
Which of the statement is/are correct?
Options- A. Only I
- B. Only II
- C. Both I and II
- D. Neither I nor II Discuss
- 6. One diagonal of a rhombus is 60% of the other diagonal. Then, area of the rhombus is how many times the square of the length of the larger diagonal?
Options- A. 1/5
- B. 2/5
- C. 6/7
- D. 3/10 Discuss
- 7. The volume of a cube is 512 cm 3, Its surface area is?
Options- A. 64 cm2
- B. 256 cm2
- C. 384 cm2
- D. 512 cm2 Discuss
- 8. The surface area of a cube is 726 m 2. Its volume is?
Options- A. 1300 m3
- B. 1331 m3
- C. 1452 m3
- D. 1542 m3 Discuss
- 9. If each side of a cube is doubled, then its volume? .
Options- A. Is doubled
- B. Becomes 4 times
- C. Becomes 6 times
- D. Becomes 8 times Discuss
- 10. Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is?
Options- A. 6 cm
- B. 8 cm
- C. 10 cm
- D. None of these Discuss
Area problems
Search Results
Correct Answer: 144 cm
Explanation:
Area of square = (Side)2 = 202
= 400 sq cm
? Area of rectangle
= 1.8 x 400 = 720 sq cm
Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720
? 5k2 = 720
? k2 = 720/5 = 144
? k = ?144 = 12 cm
Perimeter of rectangle = 2(5k + k) = 12k
= 12 x12 = 144 cm
Correct Answer: 40 cm
Explanation:
Given that, l = 2b [Here l = length and b = breadth]
Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm
According to the question,
(l - 5) (b + 5) = lb + 75
? (2b - 5) (b + 5) = 2b2 + 75 [since l = 2b]
? 5b - 25 = 75
? 5b = 100
? b = 100/ 5 = 20
? l = 2b = 2 x 20 = 40 cm
Correct Answer: 42?3 cm
Explanation:
We know that, the radius of a circle inscribed in a equilateral triangle = a/[2?3]
Where, a be the length of the side of an equilateral triangle.
Given that, area of a circle inscribed in an equilateral tringle = 154 cm2
? ?(a/2?3)2 = 154
? (a/2?3)2 = 154 x (7/22) = (7)a2
? a = 42?3 cm
Perimeter of an equilateral triangle = 3a
= 3(14?3)
= 42?3 cm
Correct Answer: y4 = 432 x2
Explanation:
Area of equilateral triangle = ?3a2/4 = x ......(i)
And perimeter = 3a = y
? a = y/3 ....(ii)
Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
?3 (y/3)2/4 = x
? x = ?3 x y2/36
? x = y2/3?3x = y2/12?3
12?3 x = y2
On squaring both sides, we get
y4 = 432x2
Correct Answer: Only I
Explanation:
Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2?r = 4a
? a = ?r/2
? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2
and area of circle = ?r2 = 3.14;r2
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2?r
? x = 2?r/3
? Area of equilateral triangle = ?3/4 x 2
= ?3/4 x 4?2r2/9
= ?2/3?3r2
= 1.89r2
Hence, Area of circle > Area of square > Area of equilateral triangle.
Correct Answer: 3/10
Explanation:
Let one diagonal be k.
Then, other diagonal = (60k/100) = 3k/5 cm
Area of rhombus =(1/2) x k x (3k/5) = (3/10)
= 3/10 (square of longer diagonal)
Hence, area of rhombus is 3/10 times.
Correct Answer: 384 cm2
Explanation:
? a3 = 512 = 8 x 8 x 8
? a = 8 cm
? Surface area = 6a2
=[6 x (8)2] cm2
=384 cm2
Correct Answer: 1331 m3
Explanation:
Surface area = 6a2 = 726
? a2 = 121
? a = 11 cm
? Volume of the cube = (11 x 11 x 11) cm3
= 1331 cm3
Correct Answer: Becomes 8 times
Explanation:
Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x3 : (2x)3
= x3 : 8x3
= 1 :8
Thus the volumes be comes 8 times.
Correct Answer: 6 cm
Explanation:
Volume of new cube = (5)3 + (4)3 + (3)3 cm3
= 126 cm3
Edge of this cube = (6 x 6 x 6)1/3 = 6 cm
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