Sol : Option 4
Let r be the radius, We have
πr2 = 4/3 πr3
⇒ r = 3/4
Q.2. The length of a garden is thrice its breadth. A playground measuring 180 sq. m occupies 1/15th of the total area of the garden. The length of the garden is
1. 60 m
2. 30 m
3. 40 m
4. 50 m
5. 90 m
Sol : Option 5
Let L be the length and B is the breadth of the garden. We have L = 3B.
Total area of the garden = 180 x 15 = 2700 sq m. ⇒ LB = 2700
⇒ 3B2 = 2700 ⇒ B2 = 900 ⇒ B = 30m
Hence the length of the garden = 30 × 3 = 90 m
Sol : Option 2
Perimeter of the equilateral triangle is 96√3 cm.
Each of the side of the equilateral triangle is 96√3 / 3 = 32√3 cm.
The height of the equilateral triangle will be = (√3 / 2) x 32√3 = 48cm
Q.4. If the ratio of radius of two spheres is 4:7, the ratio of their volume is
1. 4 : 7
2. 64 : 343
3. 49 : 16
4. 16 : 49
5. None of these
Sol : Option 2
Ratio of radii of 2 spheres is 4: 7.
∴ratio of their volume =43 : 73 = 64: 343
Q.5. The diameter (in meter) of a sphere whose volume is 268 (4/21) m3 is
1. 6
2. 12
3. 8
4. 24
5. 16
Sol : Option 3
Volume of the sphere = 268 (4/21) = 5632 / 21 m3. Now 4/3 π 3 = 5632 / 21 ⇒ r3 = (5632 / 21) x (3/4) x (7/22) = 64 ⇒ r = 4m Hence diameter = 8m
Q.6. The slant height of a right circular cone is 13 m and its height is 5 m. Find area of the curved surface.
1. 490.28 m2
2. 288.28 m2
3. 450m2
4. 200 m2
5. None of these
Sol : Option 1
Area of curved surface = πrl
Now r = √(132 - 52) = √169 - 25 = √144 = 12m
Required Area= (22/7) x 13 x 12 = 490.28m2
Q.7. Ratio of Volumes of cube and Sphere is 6/π. Find the ratio of side of cube and radius of sphere.
1. 2: 1
2. 3: 1
3. 4: 1
4. 5: 1
5. 1: 2
Sol : Option 1
Let the side of cube is 'a' and radii of sphere is 'r'.
Now Volume of cube= a3
Volume of sphere= 4/3π x r3
a3 / (4/3)π r3 = 6 / π
a / r = 2 / 1
Hence the answer is 2: 1.
Q8. What is the radius of a circle if its circumference is numerically equal to four times its area?