MCQ
Numerical: mensuration MCQ - Practice Questions with Answers
Solve 19 Numerical: mensuration questions for RAS/RPSC preparation.
Practice questions
Q1Using π = 22/7, the area of a circle of radius 14 cm is ______.
The area of a circle is πr2. Here the radius r = 14 cm and π = 22/7. So, area = 22/7 × 14 × 14. Cancel 14 with 7 to get 2, so the calculation becomes 22 × 2 × 14 = 44 × 14 = 616. Therefore, the area of the circle is 616 cm2.
Q2The length of a cold storage is double its breadth. Its height is 3 m. The area of its four walls, including the doors, is 108 m2. Find its volume.
Let the breadth be x m, so the length is 2x m and the height is 3 m. The area of the four walls is 2(l + b)h. Substituting gives 2(2x + x)3 = 18x. Since this equals 108, x = 6. The breadth is therefore 6 m and the length is 12 m. Volume is l x b x h = 12 x 6 x 3 = 216 m3. The other values do not satisfy both the wall-area condition and the given height.
Q3A solid right circular cylinder has height 17 cm and radius 8 cm. The cylinder is cut into three equal parts by two cuts parallel to the base. What is the percentage increase in total surface area?
The original total surface area of the cylinder is 2πr(h + r) = 2π × 8 × (17 + 8) = 400π. Two cuts parallel to the base create four new circular faces, each of area πr². The added area is 4π × 8² = 256π. The percentage increase is 256π/400π × 100 = 64%. The figures 50%, 68% and 79% arise from either missing some newly exposed faces or using an incorrect original surface area.
Q4The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. The area T of the triangle and the area R of the rectangle, both in square cm, satisfy the relation R = T². If the sides of the rectangle are in the ratio 1 : 3, then the length of the longer side of the rectangle is:
Let the rectangle sides be x and 3x, so its perimeter is 8x and its area is 3x². If the longer side is 27 cm, then x = 9, the rectangle perimeter is 72 cm, and the triangle perimeter is 18 cm. The equilateral triangle side is 6 cm, so its area T is 9√3. Then T² = 243, which equals the rectangle area 9 × 27. The lengths 6 cm, 9 cm, and 21 cm do not satisfy both the perimeter sum and R = T².
Q5The length, breadth and height of a room are 12 m, 9 m and 8 m respectively. The length of the longest bamboo pole that can be placed in it is:
The longest straight bamboo pole that can fit inside a rectangular room is the space diagonal of the cuboid. Its length is the square root of length squared plus breadth squared plus height squared. Here it is the square root of 12 squared plus 9 squared plus 8 squared, which is the square root of 144 plus 81 plus 64, or the square root of 289. That gives 17 m. The values 19 m and 18 m exceed the space diagonal, while 15 m is only the diagonal of the floor.
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More questions
6Match List 1 with List 2 and choose the correct option. List 1: 1. Perimeter of a square of side 12 cm; 2. Area of a rectangle of length 20 cm and breadth 11 cm; 3. Perimeter of a right triangle with sides 9 cm, 12 cm and 15 cm; 4. Circumference of a circle of radius 7 cm, using π = 22/7. List 2: P. 48 cm; Q. 36 cm; R. 220 cm2; S. 44 cm
7The total surface area of a cube is numerically equal to the volume of the cube. Find the diagonal of the cube.
8The diameter of a sphere is 8 cm. It is melted and drawn into a wire of diameter 4 mm. The length of the wire is:
9The area of a rectangular field is 300 square metres. If the length of its diagonal is 25 metres, then the perimeter of this field is:
10The inner circumference of a circular path around a circular lawn is 660 m. What is the radius, in metres, of the outer circumference of the path, if the path is 14 m wide?
11A rectangular field is 38 m long and 24 m wide. What is its perimeter?
12The area of a triangle with base 24 cm and height 15 cm is ______.
13Which one of the following statements is incorrect?
14A rectangular garden is 32 m long and 18 m wide. A wire is to be fixed around its boundary once. What length of wire is needed?
15The diameter of a garden roller is 2.8 m and its length is 4 m. If it makes 5 revolutions in 30 seconds, how much area will it cover in 5 minutes?