Area Perimeter Volume Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Find the total surface area of a cylinder with radius 7 cm and height 12 cm (use π = 22/7).
ExplanationTotal surface area = 2πrh + 2πr² = 528 + 308 = 836 cm².
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Question 2 of 50
A rectangle has an area of 96 cm² and a length of 12 cm. Find its width.
ExplanationWidth = Area/length = 96/12 = 8 cm.
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Question 3 of 50
A circular field has a radius of 21 m. Find its area (use π = 22/7).
ExplanationArea = πr² = (22/7) × 21² = (22/7) × 441 = 1,386 m².
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Question 4 of 50
Find the volume of a sphere with radius 7 cm (use π = 22/7). Round to two decimal places.
ExplanationVolume of a sphere = (4/3)πr³ = (4/3) × (22/7) × 343 ≈ 1,437.33 cm³.
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Question 5 of 50
Find the total surface area of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).
ExplanationTotal surface area = curved surface area + 2 circular ends = 440 + 2(154) = 440 + 308 = 748 cm².
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Question 6 of 50
Find the total surface area of a cuboid with length 10 cm, width 6 cm, and height 5 cm.
ExplanationSurface area = 2(lw+wh+hl) = 2(60+30+50) = 2 × 140 = 280 cm².
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Question 7 of 50
A rectangular room is 8 m long, 6 m wide, and 3 m high. Find its volume.
ExplanationVolume = length × width × height = 8 × 6 × 3 = 144 m³.
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Question 8 of 50
The area of a triangle is 48 cm² and its base is 12 cm. Find its height.
ExplanationArea = ½ × base × height, so 48 = 0.5 × 12 × h, giving h = 48/6 = 8 cm.
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Question 9 of 50
Find the area of a circle with radius 14 cm (use π = 22/7).
ExplanationArea of a circle = πr² = (22/7) × 14² = (22/7) × 196 = 616 cm².
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Question 10 of 50
Find the volume of a cone with radius 6 cm and height 7 cm (use π = 22/7).
ExplanationVolume of a cone = (1/3)πr²h = (1/3) × (22/7) × 36 × 7 = 264 cm³.
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Question 11 of 50
Find the surface area of a sphere with radius 7 cm (use π = 22/7).
ExplanationSurface area of a sphere = 4πr² = 4 × (22/7) × 49 = 616 cm².
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Question 12 of 50
A cylindrical water tank has a radius of 14 m and height of 5 m. Find its volume (use π = 22/7).
ExplanationVolume = πr²h = (22/7) × 196 × 5 = 3,080 m³.
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Question 13 of 50
Find the total surface area of a cuboid with length 8 cm, width 5 cm, and height 4 cm.
ExplanationSurface area of a cuboid = 2(lw + wh + hl) = 2(40+20+32) = 2 × 92 = 184 cm².
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Question 14 of 50
Find the area of a circle with radius 7 cm (use π = 22/7).
ExplanationArea of a circle = πr² = (22/7) × 7² = (22/7) × 49 = 154 cm².
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Question 15 of 50
Find the area of a circle with diameter 21 cm (use π = 22/7).
ExplanationRadius = 10.5 cm; Area = πr² = (22/7) × 10.5² = 346.5 cm².
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Question 16 of 50
Find the area of a triangle with a base of 10 cm and height of 6 cm.
ExplanationArea of a triangle = ½ × base × height = 0.5 × 10 × 6 = 30 cm².
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Question 17 of 50
A cube-shaped box has a side of 6 cm. Find the combined total surface area of 2 such boxes.
ExplanationSurface area of one cube = 6 × 36 = 216 cm²; two cubes = 2 × 216 = 432 cm².
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Question 18 of 50
Find the area of a parallelogram with base 12 cm and height 5 cm.
ExplanationArea of a parallelogram = base × height = 12 × 5 = 60 cm².
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Question 19 of 50
Find the area of a rhombus with diagonals of 10 cm and 12 cm.
ExplanationArea of a rhombus = ½ × d₁ × d₂ = 0.5 × 10 × 12 = 60 cm².
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Question 20 of 50
Find the curved surface area of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).
ExplanationCurved surface area of a cylinder = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
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Question 21 of 50
A rectangular garden is 20 m long and 15 m wide. Find the cost of fencing it at Rs. 50 per metre.
ExplanationPerimeter = 2(20+15) = 70 m; Cost = 70 × 50 = Rs. 3,500.
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Question 22 of 50
A rectangle has a perimeter of 60 cm and a length of 20 cm. Find its width.
ExplanationPerimeter = 2(l+w), so 60 = 2(20+w), giving 30 = 20+w, so w = 10 cm.
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Question 23 of 50
A cube has a volume of 125 cm³. Find the length of each side.
ExplanationSide = cube root of volume = ³√125 = 5 cm.
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Question 24 of 50
Find the perimeter of a rectangle with length 15 cm and width 9 cm.
ExplanationPerimeter of a rectangle = 2(length + width) = 2(15+9) = 48 cm.
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Question 25 of 50
Find the perimeter of an equilateral triangle with each side measuring 9 cm.
ExplanationPerimeter of an equilateral triangle = 3 × side = 3 × 9 = 27 cm.
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Question 26 of 50
Find the volume of a cylinder with radius 3 cm and height 7 cm (use π = 22/7).
ExplanationVolume of a cylinder = πr²h = (22/7) × 9 × 7 = 198 cm³.
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Question 27 of 50
Find the circumference of a circle with radius 7 cm (use π = 22/7).
ExplanationCircumference = 2πr = 2 × (22/7) × 7 = 44 cm.
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Question 28 of 50
Find the perimeter of a square with a side of 7 cm.
ExplanationPerimeter of a square = 4 × side = 4 × 7 = 28 cm.
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Question 29 of 50
Find the volume of a cube with a side of 4 cm.
ExplanationVolume of a cube = side³ = 4³ = 64 cm³.
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Question 30 of 50
Find the volume of a cuboid with length 6 cm, width 4 cm, and height 3 cm.
ExplanationVolume of a cuboid = length × width × height = 6 × 4 × 3 = 72 cm³.
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Question 31 of 50
Find the perimeter of a rectangle with length 12 cm and width 5 cm.
ExplanationPerimeter of a rectangle = 2(length + width) = 2(12+5) = 34 cm.
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Question 32 of 50
A cube has a total surface area of 216 cm². Find the length of each side.
ExplanationSide² = Surface area/6 = 216/6 = 36, so side = √36 = 6 cm.
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Question 33 of 50
Find the curved surface area of a cone with radius 7 cm and slant height 10 cm (use π = 22/7).
ExplanationCurved surface area of a cone = πrl = (22/7) × 7 × 10 = 220 cm².
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Question 34 of 50
Find the perimeter of a regular pentagon with each side measuring 6 cm.
ExplanationPerimeter of a regular pentagon = 5 × side = 5 × 6 = 30 cm.
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Question 35 of 50
Find the area of a rectangle with length 14 cm and width 6 cm.
ExplanationArea of a rectangle = length × width = 14 × 6 = 84 cm².
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Question 36 of 50
A rectangular water tank is 5 m long, 3 m wide, and 2 m high. Find its volume.
ExplanationVolume = length × width × height = 5 × 3 × 2 = 30 m³.
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Question 37 of 50
Find the area of a square with a side of 9 cm.
ExplanationArea of a square = side² = 9² = 81 cm².
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Question 38 of 50
Find the volume of a cuboid with length 10 cm, width 5 cm, and height 4 cm.
ExplanationVolume = length × width × height = 10 × 5 × 4 = 200 cm³.
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Question 39 of 50
Find the area of a trapezoid with parallel sides of 8 cm and 12 cm, and a height of 5 cm.
ExplanationArea of a trapezoid = ½ × (sum of parallel sides) × height = 0.5 × 20 × 5 = 50 cm².
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Question 40 of 50
Find the volume of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).
ExplanationVolume of a cylinder = πr²h = (22/7) × 49 × 10 = 1,540 cm³.
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Question 41 of 50
Find the surface area of a sphere with radius 14 cm (use π = 22/7).
ExplanationSurface area of a sphere = 4πr² = 4 × (22/7) × 196 = 2,464 cm².
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Question 42 of 50
Find the volume of a cube with a side of 10 cm.
ExplanationVolume of a cube = side³ = 10³ = 1,000 cm³.
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Question 43 of 50
Find the circumference of a circle with diameter 14 cm (use π = 22/7).
ExplanationCircumference = πd = (22/7) × 14 = 44 cm.
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Question 44 of 50
A square has a perimeter of 48 cm. Find the length of each side.
ExplanationSide = Perimeter/4 = 48/4 = 12 cm.
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Question 45 of 50
Find the total surface area of a cube with a side of 5 cm.
ExplanationSurface area of a cube = 6 × side² = 6 × 25 = 150 cm².
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Question 46 of 50
Find the area of an equilateral triangle with a side of 8 cm (use √3 ≈ 1.732).
ExplanationArea of an equilateral triangle = (√3/4) × side² = (1.732/4) × 64 ≈ 27.7 cm².
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Question 47 of 50
Find the volume of a sphere with radius 3 cm (use π ≈ 3.14). Round to two decimal places.
ExplanationVolume of a sphere = (4/3)πr³ = (4/3) × 3.14 × 27 ≈ 113.04 cm³.
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Question 48 of 50
An isosceles triangle has two equal sides of 8 cm each and a base of 5 cm. Find its perimeter.
ExplanationPerimeter = 8 + 8 + 5 = 21 cm.
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Question 49 of 50
Find the volume of a cone with radius 7 cm and height 9 cm (use π = 22/7).
ExplanationVolume of a cone = (1/3)πr²h = (1/3) × (22/7) × 49 × 9 = 462 cm³.
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Question 50 of 50
A square has an area of 64 cm². Find the length of each side.
ExplanationSide = √Area = √64 = 8 cm.
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