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A trapezium with parallel sides 10 cm and 12 cm and height 5 cm has area 55 cm², and a cylinder of radius 7 cm and height 10 cm has volume 1,540 cm³, so this Grade 8 sheet opens with the two solid-and-flat area formulas. A 1,000 L answer sits in the key.
Key Takeaways
The trapezium area is 55 cm² (Q1).
The cylinder volume is 1,540 cm³ (Q2).
Q5 records 1,000 L as a capacity answer.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The area of a trapezium with parallel sides 10 cm and 12 cm and height 5 cm is:
(a) 55 cm² (b) 60 cm² (c) 65 cm² (d) 110 cm²
2.
The volume of a cylinder with radius 7 cm and height 10 cm is:
(a) 1,540 cm³ (b) 1,440 cm³ (c) 1,540 cm² (d) 2,200 cm³
3.
The surface area of a cube of side 6 cm is:
(a) 144 cm² (b) 216 cm² (c) 256 cm² (d) 324 cm²
4.
The area of a rhombus with diagonals 8 cm and 12 cm is:
(a) 48 cm² (b) 96 cm² (c) 24 cm² (d) 60 cm²
5.
1 m³ = ?
(a) 100 L (b) 1,000 L (c) 10,000 L (d) 1,00,000 L
6.
The curved surface area of a cylinder with radius r and height h is:
(a) πr²h (b) 2πrh (c) πr² (d) 2πr²h
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Find the area of a polygon with given dimensions. A trapezium with parallel sides 15 m and 25 m and height 8 m.
8.
The base of a parallelogram is 14 cm and its area is 168 cm². Find its height.
9.
Find the total surface area of a cuboid with dimensions 8 m × 6 m × 4 m.
10.
Find the volume of a cylinder whose radius is 3.5 cm and height is 12 cm. (Use π = 22/7)
11.
The diameter of a roller is 84 cm and its length is 120 cm. Find the area it covers in 500 revolutions.
12.
A rectangular sheet of paper of size 44 cm × 20 cm is rolled to form a cylinder. Find its volume.
13.
Find the area of a quadrilateral whose diagonal is 12 cm and the perpendiculars from vertices are 5 cm and 7 cm.
14.
Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid.
Section C: Word Problems (3 Marks Each)
Apply the concepts to solve real-life problems.
15.
A water tank is 3 m long, 2 m wide, and 1.5 m deep. How many litres of water can it hold?
16.
Find the cost of painting the four walls of a room 10 m long, 8 m wide, and 5 m high at ₹50 per m².
17.
A cylindrical tank has a capacity of 3,080 m³. If its depth is 20 m, find its radius. (Use π = 22/7)
18.
A metallic cube of side 12 cm is melted and recast into a cuboid of width 8 cm and height 6 cm. Find its length.
19.
The perimeter of a trapezium is 104 m and its non-parallel sides are 18 m and 22 m. If its altitude is 16 m, find its area.
20.
A closed cylindrical tank of radius 3.5 m and height 10 m is made from sheet metal. How many m² of sheet is required?
Answer Key
1. a) 55 cm²
2. a) 1,540 cm³
3. b) 216 cm²
4. a) 48 cm²
5. b) 1,000 L
6. b) 2πrh
7. Refer to solution guide.
8. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the area of a trapezium with parallel sides 10 cm and 12 cm and height 5 cm?
55 cm², option (a) in this worksheet (Q1).
What is the volume of a cylinder of radius 7 cm and height 10 cm?
1,540 cm³, option (a) in this worksheet (Q2).
How many litres in 1 m³?
1,000 L, option (b) in this worksheet (Q5).