WORKSHOP -SOLIDS -27-05-2025

Multiple Choice

Which of the following best defines volume?

• Area covered by an object
• Weight of a 3D object
• Space occupied by a 3D object
• Surface texture of an object

Explanation Slide...

Volume is the measure of the three-dimensional space occupied by a solid.

Multiple Choice

A cube has how many total faces, edges, and corners?

• 6 faces, 12 edges, 8 corners
• 4 faces, 8 edges, 6 corners
• 6 faces, 8 edges, 12 corners
• 8 faces, 12 edges, 6 corners

Explanation Slide...

A cube has 6 square faces, 12 edges, and 8 vertices (corners).

Multiple Choice

The formula for the total surface area of a cube with side ‘a’ is:

• 4a²
• 2a²
• 6a²
• a³

Explanation Slide...

Each of the 6 faces of a cube is a square with area a², so T.S.A = 6a².

Multiple Choice

The volume of a rectangular prism (cuboid) is calculated by:

• l × b
• 2(l+b)
• l × b × h
• (l + b + h)²

Explanation Slide...

Volume = length × breadth × height for a rectangular solid.

Multiple Choice

Volume of a pyramid with rectangular base is:

• l × b × h
• ½ l × b × h
• (1/3) l × b × h
• (2/3) l × b × h

Explanation Slide...

For pyramids, volume = (1/3) × base area × height.

Multiple Choice

Which of the following gives the lateral surface area of a cylinder?

• 2πr²
• πr²
• πr(r + h)
• 2πrh

Explanation Slide...

Lateral surface area (curved area) of a cylinder = 2πrh.

Multiple Choice

What is the volume of a cone with base radius ‘r’ and height ‘h’?

• πr²h
• ½ πr²h
• (1/3) πr²h
• πr h

Explanation Slide...

Volume of a cone = (1/3) × π × r² × h.

Multiple Choice

Total surface area of a sphere is given by:

• 4πr
• πr²
• 3πr²
• 4πr²

Explanation Slide...

A sphere has only a curved surface with area 4πr².

Multiple Choice

A frustum of cone is formed by:

• Merging two cones
• Cutting a cone horizontally
• Bending a cylinder
• Cutting a pyramid vertically

Explanation Slide...

A frustum is formed when a cone or pyramid is cut parallel to its base, removing the top.

Multiple Choice

What is the part of a circle bounded by an arc and a chord called?

• Sector
• Tangent
• Segment
• Diameter

Explanation Slide...

A segment is the region between a chord and the corresponding arc of a circle.

Multiple Choice

A rectangular park is 250 m long and 150 m wide. A person walks around it 3 times. What is the total distance covered?

• 600 m
• 1200 m
• 2400 m
• 3000 m

Explanation Slide...

Perimeter = 2(l + b) = 2(250 + 150) = 800 m; Total distance = 800 × 3 = 2400 m.

Multiple Choice

If the breadth of a rectangle is 1/3rd of its length and the perimeter is 40 m, find its area.

• 50 m²
• 75 m²
• 95 m²
• None of these

Explanation Slide...

Let length = x, then breadth = x/3. Perimeter = 2(x + x/3) = 40 → x = 15. Area = 15 × 5 = 75 m².

Multiple Choice

Which of the following is the correct formula for the total surface area of a cube with side length 'a'?

• 6a^2

• 4a^2

• a^3

• 12a

Multiple Choice

Find the side of a cube, if its surface area is 216 cm².

• 6
• 8
• 9
• 12

Explanation Slide...

TSA of cube = 6a² → 6a² = 216 → a² = 36 → a = 6 cm.

Multiple Choice

Which of the following formulas correctly represents the total surface area (T.S.A) of a cuboid?

• 2lb + 2lh + 2bh

• 2πrh

• πr² + πrl

• 4πr²

Explanation Slide...

Area = ½ × (a + b) × h = ½ × (20 + 18) × 15 = 285 cm².

Open Ended

Explain the difference between the formulas for the total surface area of a cylinder and a cone.

Multiple Choice

Find the area of a trapezium whose parallel sides are 20 cm and 18 cm long and the distance between them is 15 cm.

• 225 cm²
• 275 cm²
• 285 cm²
• 315 cm²

Multiple Choice

What is the area of a circle with a radius of ‘r’?

• πr²

• πr/2

• 2πr

• 4πr

Multiple Select

Which of the following are correct formulas for the volume of the given solids?

• Cuboid: l × b × h

• Cylinder: πr²h

• Cone: (1/3)πr²h

• Sphere: (4/3)πr³

Multiple Choice

What is the total surface area (T.S.A) of a hemisphere with radius r?

• 3πr²

• 4πr²

• 2πr²

• πr²

Multiple Choice

What is the formula for the volume of a cube?

• a^3

• 6a^2

• 4a^2

• a^2

Multiple Choice

Which formula represents the volume of a frustum of a cone?

• (1/3)πh(R^2 + r^2 + Rr)

• π(R+r) × l

• π(R+r) × l + πR^2 + πr^2

• √[h^2 + (R - r)^2]