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\ 03-Jan-2025 Bharat Arora Proof-3 Reader’s Sign _______________________ Date __________

B. Fill in the blanks.

1. The coefficient of –99xyz is .................

2. Volume of a rectangular box with length 3x, breadth 4y, and height 5z is .................

3. Top view of the given prism (alongside) is a .................
4. Pentagonal prism can have ................. pentagons.

5. The area of a trapezium is 256 cm and the sum of its parallel sides is 32 cm,
2
then the distance between its parallel sides is .................

C. State whether the following statements are True (T) or False (F).

1. The Euler’s formula holds for F = 6, E = 12 and V = 8.
2. The regular convex polyhedrons are known as platonic solid.

3. The number of edges in a sphere is 1.

4. A cube is a special type of cuboid.

5. If x + y = 26 and xy = 6, then x – y = 14.
2
2
D. Attempt the following questions.
1. What should be added to (–a + b + c) to obtain a(a + b + c) – b(a – b + c)?

1 1
2
2. Find the value of 64x + if 8x + = 10 .
64x 2 8x
3. Divide x + 3x – 4x – 6 by (x + 1) using a long division method.
2
3
4. The perimeter of a triangle is 16x – 20x + 12. If two of its sides are 5x + 8x – 3 and
2
2
8x – 3x + 12, find its third side.
2
5. Verify Euler’s formula for a dodecahedron.
6. A cuboidal box is of dimensions 80 cm × 144 cm × 16 cm. How many small cubical boxes

with side 8 cm can be placed in the given cuboid?
7. Find the capacity of a water tank, in litres, whose dimensions are 4.2 m, 3 m and 12.8 m.

8. The ratio of radii of two cylinders is 2 : 3 and the ratio of their heights is 1 : 32. What will
be the ratio of their volumes?

261 Unit Test – 3