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.
Solution: 3.61492 x 106
= 3.61492 x 1000000
= 3614920
3. Express 0.00000000837 in standard form.
0.00000000837
= 0.00000000837 x 109 / 109
= 8.37 ×10-9
2. Simplify [25 x t-4]/[5-3 x 10 x t-8]
Solution:
We can write the given expression as;
[52x t-4]/[5-3 x 5 x 2 x t-8]
= [52 x t-4+8]/[5-3+1 x2]
= [52+2 x t4]/[2]
= [54 x t4]/[2]
= [625/2] t4
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°
4. In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint: Draw a line parallel to ST through point R.]
Solution:
First, construct a line XY parallel to PQ.
As we know, the angles on the same side of the transversal are equal to 180°.
So, ?PQR + ?QRX = 180°
Or,?QRX = 180° – 110°
? ?QRX = 70°
Similarly,
?RST + ?SRY = 180°
Or, ?SRY = 180° – 130°
? ?SRY = 50°
Now, for the linear pairs on the line XY-
?QRX + ?QRS + ?SRY = 180°
Substituting their respective values we get,
?QRS = 180° – 70° – 50°
Or, ?QRS = 60°
3. In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
Solution:
Since AB || CD GE is a transversal.
It is given that ?GED = 126°
So, ?GED = ?AGE = 126° (alternate interior angles)
Also,
?GED = ?GEF + ?FED
As
EF ? CD, ?FED = 90°
? ?GED = ?GEF + 90°
Or, ?GEF = 126° – 90° = 36°
Again, ?FGE + ?GED = 180° (Transversal)
Substituting the value of ?GED = 126° we get,
?FGE = 54°
So,
?AGE = 126°
?GEF = 36° and
?FGE = 54°
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