Answer: A
Explanation:
Ratio of areas = (ratio of radii)Â²
\( \frac {16}{1} \) = (ratio of radii)Â²
ratio of radii = \( \frac {4}{1} \)
The required radius = 16 m
Q2. What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?
Answer: C
Explanation:
\( \pi RÂ² = \pi r1Â² + \pi r2Â² \)
\( \pi RÂ² = \pi (r1Â² + r2Â²) \)
RÂ² = (400 + 441)
R = 29
Q3. Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.
Answer: A
Explanation:
r = 20 ; h = 21
l = \( \sqrt {(400 + 441)} \)= 29 cm
Total surface area = \( \pi rl + \pi rÂ² \)
= \( \pi r(l + r) \)
= \( \frac {22}{7} \times 20(49) \)
= 3080 cmÂ²
Q4. A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter by 54 cm and the length of the tube be 490 cm, find the volume of plastic.
Answer: B
Explanation:
External Radius = 27;
Internal Radius = 23
Volume of Plastic = \( \pi h(RÂ² â€“ rÂ²) = \frac {22}{7} \times 490(27Â² â€“ 23Â²) = 308000 cmÂ³ \)
Q5. A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?
Answer: D
Explanation:
Number of cones = \( \frac {Volume of Cylinder}{Volume of one cone} \)
= \( \frac {\pi \times 5 \times 5 \times 7} {( \frac {1}{3} \pi \times \frac {1}{10} \times \frac {1}{10} \times 1)} \)
= 52500
Answer: C
Explanation:
length = \( 2x \)
height = \( 3x \)
Area of the wall = \( 3x \times 2x = 6xÂ² \) = 600
\( x \) = 10;
Sum of the length and height of the wall = 50
Q2. If the area of a circle is 616cmÂ² whose diameter is equal to the radius of a semicircle. Find the perimeter of the semicircle?
Answer: C
Explanation:
Area of a circle = 616cmÂ²
\( \pi rÂ² = 616; \)
r = 14
D = Radius of Semi Circle = 28
Perimeter of the semicircle = \( \pi r + 2r \)= 144 cm
Q3. One side of the rectangular ground is 8m and its diagonal is 17m. Find the area of the ground?
Answer: D
Explanation:
d = \( \sqrt {(lÂ² + bÂ²)} \)
17 = \( \sqrt {(lÂ² + 8Â²)} \)
lÂ² = 17Â² â€“ 8Â² \( \Rightarrow \)l = 289 â€“ 64 = 225
l = 15
Area = \( 15 \times 8 \)= 120 mÂ²
Q4. The side of a squareshaped garden is 8âˆš2. Find the maximum possible distance between any two corners
Answer: C
Explanation:
d = a \( \sqrt {2} \)
a = 8\( \sqrt {2} \)
d = 16m
Q5. A rectangular ground 16m long and 10m breadth. It has a gravel path 2.5m wide all around it on the outside. What is the area of the path?
Answer: B
Explanation:
Area of ground = \( 16 \times 10 \) = 160
Total area (ground + path) = \( (16 + 5) \times (10 + 5) \) = 315
Area of path = 315 â€“ 160 = 155 mÂ²
Answer: B
Explanation:
Area of the plot = \( 1.3 \times 1.3 = 1.69 = 69 % \)
Q2. A ladder is resting with one end in contact with the top of the wall of height 15m and the other end of the ground is at a distance 8m from the wall. The length of the ladder is?
Answer: A
Explanation:
Hypotenuse = \( \sqrt {(base)Â² + (altitude)Â²} \)
\( \sqrt {(8)Â² + (15)Â²} = \sqrt {289} \) = 17 m
Q3. The perimeter of a square is equal to twice the perimeter of a rectangle of length 10 cm and breadth 4 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square?
Answer: D
Explanation:
Perimeter of square = 2(l + b)
= \( 2 \times 2(10 + 4) = 2 \times 28 \) = 56 cm
Side of square = \( \frac {56}{4} \) = 14 cm
Radius of semi circle = \( \frac {14}{2} \) = 7cm
Circumference of the semicircle = \( \frac {22}{7} \times 7 + 14 \) = 36 cm
Q4. The length of a rectangle is \( \frac {3}{{5}^{th}} \) of the side of a square. The radius of a circle is equal to the side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
Answer: C
Explanation:
Circumference of the circle = 132
\( 2 \pi R \) = 132;
R = 21 cm
Side of square = 21 cm
Length of the rectangle = \( \frac {3}{5} \times 21 = \frac {63}{5} \)
Area of the rectangle = \( \frac {63}{5} \times 15 \) = 189 cmÂ²
Q5. Smallest side of a rightangled triangle is 13 cm less than the side of a square of perimeter 72 cm. The secondlargest side of the rightangled triangle is 2 cm less than the length of the rectangle of area 112 cmÂ² and breadth 8 cm. What is the largest side of the rightangled triangle?
Answer: D
Explanation:
Side of square = \( \frac {72}{4} \) = 18 cm
Smallest side of the right angled triangle = 18 â€“ 13 = 5 cm
Length of rectangle = \( \frac {112}{8} \) = 14 cm
Second side of the right angled triangle = 14 â€“ 2 = 12 cm
Hypotenuse of the right angled triangle = \( \sqrt {(25 + 144)} \) = 13cm
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