Surface Area, Volume and Capacity — Practice Quiz
ICSE · Class 8 · Mathematics
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A closed wooden box has external dimensions 30 cm by 18 cm by 20 cm and wall thickness 1.5 cm throughout. Find its capacity.
A cuboid has dimensions 4 cm, 10 cm and 14 cm. Another cuboid has dimensions 8 cm, 8 cm and 10 cm. A third cuboid has dimensions 4 cm, 6 cm and 22 cm. All three are melted to form one cube. Find the edge of the cube.
A rectangular room is 6 m long, 5.2 m broad and 4.5 m high. It has two doors of size 1.2 m by 2 m and three windows of size 1 m by 80 cm. Find the total internal area to be whitewashed, including the roof.
A cuboid has length 30 cm, breadth 25 cm and height 20 cm. Find its total surface area and volume.
Sample Questions
Three cubes of edge 8 cm are joined in a row to form a cuboid. Find the total surface area and the volume of the cuboid, and identify the correct pair.
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Total surface area = 896 cm², Volume = 1536 cm³
Step 1: The cuboid formed has length 3 × 8 = 24 cm, breadth 8 cm, and height 8 cm. Step 2: Total surface area = 2(lb + bh + hl) = 2(24 × 8 + 8 × 8 + 8 × 24) = 2(192 + 64 + 192) = 2 × 448 = 896 cm². Step 3: Volume = l × b × h = 24 × 8 × 8 = 1536 cm³. Both statements are correct.
A cube has edge 12 cm. Find its total surface area, volume and diagonal, and choose the correct pair of surface area and diagonal.
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Total surface area = 864 cm², Diagonal = 20.784 cm
Step 1: Total surface area of a cube = 6a² = 6 × 12² = 6 × 144 = 864 cm². Step 2: Diagonal of a cube = edge × √3 = 12 × 1.732 = 20.784 cm. These two statements are correct.
A cube has total surface area 294 cm². Find its volume.
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343 cm³
Step 1: Total surface area of a cube = 6a². So, 6a² = 294. Step 2: a² = 294 ÷ 6 = 49. Step 3: a = 7 cm. Step 4: Volume = a³ = 7³ = 343 cm³. So the correct answer is 343 cm³.
A cylinder has radius 7 cm and height 10 cm. Take π = 22/7. Find its volume.
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1540 cm³
Step 1: Volume of a cylinder = πr²h. Step 2: Substitute the values. Volume = 22/7 × 7² × 10 = 22/7 × 49 × 10 = 22 × 7 × 10 = 1540 cm³. So the correct answer is 1540 cm³.
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