3. One angle of a six-sided polygon is 140o and the other angles are equal. Find the measure of each equal angle.
Solution:
Let the measure of each equal angles are x.
Then we can write
140o + 5x = (2 × 6 – 4) × 90o
140o + 5x = 720o
5x = 580o
x = 116o
Therefore, the measure of each equal angles are 116o
2. The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5. Find each angle of the pentagon.
Let the angles of the pentagon are 4x, 8x, 6x, 4x and 5x.
Thus, we can write
4x + 8x + 6x + 4x + 5x = 540o
27x = 540o
x = 20o
Hence the angles of the pentagon are:
4×20o = 80o, 8×20o = 160o, 6×20o= 120o, 4×20o= 80o, 5×20o= 100o
1. The sum of the interior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon.
4. The length, breadth and height of cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2, find its volume.
720 cubed cm
3. The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
2. The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
14 cm
1. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
6 m
4. The length of a hall is double its breadth. Its height is 3 m. The area of its four walls (including doors and windows) is 108 m2, find its volume.
Solution:
3. A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new cube? Also, find the ratio between the surface area of the original cube and the total surface area of all the small cubes formed.
Solution:
2. The diameter of a garden roller is 1.4 m and it 2 m long. Find the maximum area covered by it 50
Solution: