Topics |
|---|
1. A Sector of with circle of radius 10 cm has central angle of 72° . Find the area of the sector
Given radius (r) = 10 cm, Central angle θ = 72°
2. If the area of a Sector is 
of the area of the circle, then what is the measure of the corresponding central angle?
Here, Area of the Sector = of the area of the circle
Area of the Sector = 
x Area of the circle
12 x Area of the Sector = Area of the circle → (1)
3. In a clock, the minute hand is of length 14 cm. Find the area covered by the minute hand in 5 minutes.
Note that in 60 minutes the minute hand rotates through 360°
4. The radius of the circle is 3.5cm and the area of Sector is 3.85 sq.cm. Find the measure of the arc of the circle?
Given : Radius of circle (r) = 3.5 cm.
Area of the Sector (A) = 3.85 cm2
By substituting given values
5. Find the area of the Sector of a Circle of radius 6 cm and arc with length 15 cm.
Given : Radius of the circle (r) = 6cm
Length of an arc (l) = 15 cm
Area of the Sector (A) = 
x length of an arc
Area of the Sector (A) = 
x 15
= 45 cm2
6. The diameter of a circle is 10 cm. Find the length of the arc, when the corresponding central angle is 45°
Given diameter = 10 cm; the radius r = 5 cm
Central angle θ = 45°
Length of the arc
7. Find the angle Subtended at the centre of a circle by an arc for the following :
radius of circle = 5.5 m, length of arc = 6.05 m.
r = 5.5m, l = 6.05 m
8. The radius of a circle is 7 cm. Find area of the Sector of this circle if the corresponding angle is 30°
r = 7 cm, θ = 30°
Area of the Sector
9. Find the length of the arc of a circle with radius 0.7 m and area of the Sector is 0.49 m2
r = 0.7 m, Area of Sector = 0.49 m2
10. The length, breadth and height of a cuboid 10 cm,6cm and 13 cm respectively. Find its total surface area.
Given : length (l) = 10cm, breadth (b) = 6 cm and height (h) = 13 cm.
Total Surface area of a cuboid = 2(lb + bh + lh)
= 2(10x6 + 6x13 + 10x13)
= 2(60 + 78 + 130)
= 2(268)
= 536 cm2
11. The total surface area of a cuboid is 166 cm2. Find its length if breadth and height are 5 cm and 4 cm respectively.
Given : breadth (b) = 5 cm, height (h) = 4 cm and total Surface area = 166 cm2
Total Surface area of a cuboid = 2(lb+bh+lh)
166 = 2 ( l x 5 + 5 x 4 + l x 4 )
166 = 2 (9 l + 20)
l = 7cm
12. The dimension of a cuboid in cm are 20 x 18 x 10. Find its volume.
Given l = 20cm, b = 18cm, and h = 10 cm
Volume of the cuboid = l x b x h
= 20 x 18 x 10
= 3600 cm3
13. A container used for transportation has capacity 34.5m3. The length and breadth of the container are 5m and 2.3m respectively. Find the height of the container.
Given : Volume (v) = 34.5m3, length (l) = 5m and breadth (b) = 2.3m
Volume of a cuboid = l x b x h
34.5 = 5 x 2.3 x h
h = 3m
14. Find the total Surface area of a cube with side 9cm.
Given : l = 9cm
Surface area of a cube = 6 l2
= 6 x 92
= 486
Total surface area of the cube is 486 cm2
15. Find the Volume of a cube with side 5.2cm.
Given l = 5.2cm
Volume of the cube = l3
= 5.23
= 140.608
= 140.61cm3
16. Find the volume of a cube having total Surface area as 661.5cm2
Given : Total Surface area = 661.5cm2
Surface area of a cube = 661.5cm2
6 l2 = 661.5
l2 = 110.25
l = 10.5
Volume of cube = l3
= (10.5)3
= 1157.625cm3
17. Two cubes, each with 12cm edge, are joined end to end. Find the Surface area of the resulting cuboid.
For each cube, Side = 12cm
For the resulting cuboid
l = (12 + 12)cm = 24cm; b = 12cm and h = 12cm
Total surface area of a cuboid = 2 (lb + bh + lh)
= 2 (24 x 12 + 12 x 12 + 24 x 12)
= 2 (288 + 144 + 288)
= 2 (720)
= 1440sq.cm
18. The dimensions of a cuboid in cm are 16 x 14 x 20. Find its total Surface area.
Given l = 16cm, b = 14cm, h = 20cm
Total Surface area = 2 (lb + bh + lh)
= 2 (16 x 14 + 14 x 20 + 20 x 16)
= 2 (224 + 280 + 320)
= 2 (824)
= 1648 cm2
19. The side of a cube is 60cm. Find the total Surface area of the cube
Given : Side (l) = 60cm
Total surface area = 6 l2
= 6 x (60)2
= 6 x 3600
= 21600 cm2
20. The value of a cube is 1000cm3. Find its total Surface area.
Given : Volume = 1000cm3
l3 = 1000cm3
l = 10cm
Total Surface area = 6 l2
= 6 x (10)2
= 600cm2
Practice in Related Chapters |
| Trignometry |
| Arithemetic Progression and Geometric Progression |
| Mensuration |
