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:
1. In a building, there are 24 cylindrical pillars. For each pillar, radius is 28 m and height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.
Solution:
4. Write 3.61492 x 106 in usual form.
3. Express 0.00000000837 in standard form.
2. Simplify [25 x t-4]/[5-3 x 10 x t-8]
1.If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?
5. In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δ XYZ, find ∠OZY and ∠YOZ.
As we know, the sum of the interior angles of the triangle is 180°.
So, ?X +?XYZ + ?XZY = 180°
substituting the values as given in the question we get,
62° + 54° + ?XZY = 180°
Or, ?XZY = 64°
Now, As we know, ZO is the bisector so,
?OZY = ½ ?XZY
? ?OZY = 32°
Similarly, YO is a bisector and so,
?OYZ = ½ ?XYZ
Or, ?OYZ = 27° (As ?XYZ = 54°)
Now, as the sum of the interior angles of the triangle,
?OZY +?OYZ + ?O = 180°
Substituting their respective values we get,
?O = 180° – 32° – 27°
Or, ?O = 121°
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