Test: Surface Area, Volume and Capacity - Grade 8 MCQ

The total surface area of a cube is given by 6a². Setting 6a² = 216 gives a² = 36, so a = 6 cm. Each edge of the cube is 6 cm long.

The volume of a cube is calculated using the formula Volume = a³, where 'a' is the length of one edge. This formula highlights the property of cubes where all sides are equal.

The total surface area of a cylinder is given by the formula Total Surface Area = 2πrh + 2πr², which includes both the curved surface area and the areas of the two circular bases.

First, calculate the external volume: 12 × 10 × 8 = 960 cm³. Then, calculate the internal dimensions: 10 × 8 × 6 = 480 cm³. The volume of the material is 960 - 480 = 480 cm³.

Volume refers to the total space occupied by the solid material of the container, while capacity refers specifically to the internal volume available for holding liquids or gases.

The volume of the block is calculated as Volume = Length × Width × Height = 10 cm × 5 cm × 2 cm = 100 cm³.

Let the dimensions be 2x, 3x, and 4x. The volume V = 2x × 3x × 4x = 24x³. Setting 24x³ = 120 gives x³ = 5, thus x = 1.71. The longest side = 4x = 6.86 cm, rounding gives approximately 8 cm.

The curved surface area is calculated using the formula 2πrh. Substituting the values, Curved Surface Area = 2 × π × 3 cm × 12 cm = 226.08 cm².

The total surface area is calculated by the formula 2(lb + bh + hl). Substituting gives 2(2 × 3 + 3 × 4 + 4 × 2) = 2(6 + 12 + 8) = 2(26) = 52 m².

The volume of a cuboid is calculated using the formula Volume = Length × Width × Height. This formula reflects the three dimensions of the cuboid, allowing us to determine the total space it occupies.

Since 1 liter is equivalent to 1,000 cm³, a capacity of 2 liters equals 2 × 1,000 cm³ = 2,000 cm³. This conversion is crucial in various applications, including cooking and laboratory settings.

The total surface area of a cube is calculated using the formula Total Surface Area = 6 × (Edge Length)². For a cube with an edge of 4 cm, the total surface area is 6 × (4 cm)² = 6 × 16 cm² = 96 cm².

The formula for volume is V = πr²h. Rearranging gives r = √(V/(πh)). Substituting the values, r = √(1050/(π × 15)) ≈ 7 cm.

The total surface area of the walls is calculated as 2(l × h) + 2(b × h). Using the dimensions, Total Surface Area = 2(5 × 3) + 2(4 × 3) = 30 + 24 = 54 m².

Volume is generally expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). This measurement accounts for the three-dimensional space an object occupies.

1 cubic meter is equivalent to 1,000 liters. This equivalence is important in conversions for various applications, particularly in water storage and utility measurements.

To find the internal volume, first calculate the internal dimensions: Length = 30 - 2(1) = 28 cm, Breadth = 20 - 2(1) = 18 cm, Height = 15 - 2(1) = 13 cm. Therefore, the internal volume = 28 × 18 × 13 = 6,072 cm³.

The area of the walls is calculated as 2 × (Length + Width) × Height = 2 × (4 + 5) × 3 = 54 m².

The volume of a cylinder is given by V = πr²h. Using π ≈ 3.14, V = 3.14 × (7 cm)² × 10 cm = 3.14 × 49 × 10 ≈ 1539.4 cm³, which rounds to approximately 1540 cm³.

To find the internal dimensions, subtract twice the thickness from each external dimension: Length = 50 - 2(3) = 44 cm, Breadth = 40 - 2(3) = 34 cm, Height = 30 - 2(3) = 24 cm.