Mensuration Worksheet

Objective Type Questions

1. State true or false.
   (a)The lateral surface area of a cylinder includes the top and bottom faces of the cylinder.
   
   (b)1 ml³ = 1 cm³
   
   Multiple Choice Questions
   
   
2. Which of the following statement is INCORRECT?
   (a)Perimeter of a square is measured in units.
   (b)Volume of a solid is measured in cubic units.
   (c)Area of a rectangle is measured in square units.
   (d)Surface area of a solid is measured in cubic units.
   
   
3. The volume of the following cuboid whose length is twice the height and breadth is half the height is 
   (a) 3y³ cubic units
   (b) 2y³ cubic units
   (c) y³ cubic units
   (d) y² cubic units
   
   
   
4. Area of a polygon can be found by using which of the following the parameter?
   (a)angle
   (b)size
   (c)length
   (d)curve
   
   
5. If a rectangular piece of paper with dimensions 66 cm × 21 cm is rolled along its length to form a cylinder, then the radius of the cylinder thus formed is  (Use p = 22/7)
   (a)9 cm
   (b)9.5 cm
   (c)10 cm|
   (d)10.5 cm
   
   
6. 1 m³ = 1000 litre, then 505.7 m³ = ______________ kl
   (a)505.7
   (b)5057
   (c)50570
   (d)50570
   
   
7. The change in the volume of a cube when its side becomes 5 times the original side is
   (a)25 times the original volume
   (b)  times the original volume
   (c)125 times the original volume
   (d)  times the original volume
   
   
8. The volume of cylinder is equal to
   (a)Area of the base × height
   (b)Area of the base + height
   (c)2(Area of the base) × height
   (d)2(Area of the base) + height
   
   
9. The area of four walls of following cuboid is
   (a)[2(a + b + h)] square units
   (b)(a × b × h) square units
   (c)(2 × a × b × h) square units
   (d)[2(a + b) × h] square units
   
   
   Subjective Questions
   
   
10. Find the area of pentagon ABCDE.
    
    
    
11. If you need to find the area of following polygon, show that in how many different ways you can divided it into different geometric shapes.
     
    
    
12. Find the volume of cylinder formed by rolling the following rectangular paper along its breadth. (Use p = 22/7)
    
    
    
13. Find the area of the shaded region ABR.
    
    
    
14. Divide the following shape into three triangles.
    
    
    
    
15. The floor of a hall consists of 300 rectangular-shaped tiles of dimensions 18 cm × 10 cm. Find the cost of polishing the floor at the rate of Rs. 6 per metre square. 
    
    
16. The diameter of a 140 cm long garden roller is 68 cm. How much area can it level in 100 revolutions? (Use p = 22/7)
    
    
    
17. It is Meena’s birthday and she ordered 2-layer birthday cake as follows:
    Dimensions of the bottom layer cake are 15 cm × 15 cm × 10 cm and that of a top layer cake are 12 cm × 12 cm × 6 cm. Find the volume of the whole cake.
    
    
    
18. The weight of a cuboidal metal box of dimensions 4.5 m × 4 m × 3 m is 12 kg. Find the weight of the box of dimensions 6 m × 2.5 m × 3 m of same metal.
    
    
19. The radius of following pillar is 14 cm and height is 6 m. It is painted with golden colour and cost of painting is Rs. 16 per m2. What can be the cost of painting 30 such pillars. (Use p = 22/7)
    
    
    
20. Four small equal rectangles are cut off from each corner of a big rectangle. Find the area of portion left after removing them.
    
    

Objective Type Questions

1. State true or false.
   (a)The lateral surface area of a cylinder includes the top and bottom faces of the cylinder.
   
   (b)1 ml³ = 1 cm³
   Solution:
   (a)False
   The lateral surface area of a cylinder excludes the top and bottom faces of the cylinder. If its top and bottom faces are included, it becomes total surface area.
   
   (b)False
   1 cm³ = 1 ml
   
   Multiple Choice Questions
   
   
2. Which of the following statement is INCORRECT?
   (a)Perimeter of a square is measured in units.
   (b)Volume of a solid is measured in cubic units.
   (c)Area of a rectangle is measured in square units.
   (d)Surface area of a solid is measured in cubic units.
   Correct option: (d) Surface area of a solid is measured in cubic units.
   Solution:
   Surface area of a solid is measured in square units.
   
   
3. The volume of the following cuboid whose length is twice the height and breadth is half the height is 
   (a) 3y³ cubic units
   (b) 2y³ cubic units
   (c) y³ cubic units
   (d) y² cubic units
   
   Correct option: (c) y³ cubic units
   Solution:
   Height of a cuboid = y units
   Then,
   length of a cuboid = 2y units
   breadth of a cuboid =  units
   Therefore, volume of a cuboid = length × breadth × height  cubic units
   
   
4. Area of a polygon can be found by using which of the following the parameter?
   (a)angle
   (b)size
   (c)length
   (d)curve
   Correct option: (c) length
   Solution:
   The length of a polygon is used to find the area of a polygon.
   
   
5. If a rectangular piece of paper with dimensions 66 cm × 21 cm is rolled along its length to form a cylinder, then the radius of the cylinder thus formed is  (Use p = 22/7)
   (a)9 cm
   (b)9.5 cm
   (c)10 cm|
   (d)10.5 cm
   Correct option: (d) 10.5 cm
   Solution:
   Circumference of the base of cylinder = 66 cm
   
   
   
6. 1 m³ = 1000 litre, then 505.7 m³ = ______________ kl
   (a)505.7
   (b)5057
   (c)50570
   (d)50570
   Correct option: (a) 505.7
   Solution:
   1 m³ = 1000 litre = 1 kl
   Then, 505.7 m³ = 505.7 kl
   
   
7. The change in the volume of a cube when its side becomes 5 times the original side is
   (a)25 times the original volume
   (b)  times the original volume
   (c)125 times the original volume
   (d)  times the original volume
   Correct option: (c) 125 times the original volume
   Solution:
   Let the side of a cube = a
   Then, volume of cube = a³
   Length of side of new cube = 5a
   Then, volume of new cube = (5a)³ = 125a³ = 125 × original volume
   
   
8. The volume of cylinder is equal to
   (a)Area of the base × height
   (b)Area of the base + height
   (c)2(Area of the base) × height
   (d)2(Area of the base) + height
   Correct option: (a) Area of the base × height
   Solution:
   Let r be the radius of the cylinder and h be its height.
   Then, volume of a cylinder = pr² × h = area of the circular base × height
   
   
9. The area of four walls of following cuboid is
   (a)[2(a + b + h)] square units
   (b)(a × b × h) square units
   (c)(2 × a × b × h) square units
   (d)[2(a + b) × h] square units
   
   Correct option: (d) 2(a + b) × h square units
   Solution:
   The area of the four walls is given by product of Height and Perimeter of the floor.
   Therefore, area of four walls = c × 2(a + b)
   
   Subjective Questions
   
   
10. Find the area of pentagon ABCDE.
    
    
    Solution:
    Area of rectangle ABCD = 9 cm × 5 cm = 45 cm²
    Area of triangle AED 
    Therefore, area of pentagon ABCDE = Area of rectangle ABCD – Area of triangle AED
    = (45 – 6) cm²
    = 39 cm²
    
    
11. If you need to find the area of following polygon, show that in how many different ways you can divided it into different geometric shapes.
     
    Solution:
    The given polygon can be divided in two different ways as follows:
    Type 1:
    ΔABF, Rectangle BCEF and ΔCDE
    
    Type 2:
    Trapezium ABCD and trapezium AFED.
    
    
    
12. Find the volume of cylinder formed by rolling the following rectangular paper along its breadth. (Use p = 22/7)
    
    Solution:
    As a rectangular paper is rolled along its breadth, it forms a curved surface of cylinder with base circumference as 14 m and height as 88 m.
         
    Circumference of the base of cylinder = 14 m
    
    
    
13. Find the area of the shaded region ABR.
    
    Solution:
    Area of rectangle PQRS = PQ × QR = 20 × 8 = 160 cm²
    Area of triangle AQR =  × AQ × RQ =  × 18 × 8 = 72 cm²
    Area of triangle BSR =  × SR × BS =  × 20 × 1.5 = 15 cm²
    Area of triangle APB =  × AP × PB =  × (20 – 18) × (8 – 1.5) = 6.5 cm²
    Now, area of shaded region ABR = Area of rectangle PQRS – (Area of triangle AQR + Area of triangle BSR + Area of triangle APB)
    = 160 – (72 + 15 + 6.5)
    = 160 – 93.5
    = 66.5 cm² 
    
    
14. Divide the following shape into three triangles.
    
    Solution:
    The given shape can be divided into three triangles as follows:
    
    
    
15. The floor of a hall consists of 300 rectangular-shaped tiles of dimensions 18 cm × 10 cm. Find the cost of polishing the floor at the rate of Rs. 6 per metre square. 
    Solution:
    Area of one rectangular-shaped tile = 18 cm × 10 cm = 180 cm²
    Then, area of 300 rectangular-shaped tiles = 300 × 180 cm = 54000 cm2 = 540 m²
    Therefore, cost of polishing 540 m² = Rs. 6 × 540 = Rs. 3240 
    
    
16. The diameter of a 140 cm long garden roller is 68 cm. How much area can it level in 100 revolutions? (Use p = 22/7)
    
    Solution:
    Curved surface area of a roller 
    Area that can be level in 100 revolutions = 100 × 12320 = 1232000 m²
    
    
17. It is Meena’s birthday and she ordered 2-layer birthday cake as follows:
    Dimensions of the bottom layer cake are 15 cm × 15 cm × 10 cm and that of a top layer cake are 12 cm × 12 cm × 6 cm. Find the volume of the whole cake.
    
    Solution:
    Volume of the bottom layer cake = 15 cm × 15 cm × 10 cm = 2250 cm³
    Volume of the top layer cake = 12 cm × 12 cm × 6 cm = 864 cm³
    Therefore, volume of the whole cake = 2250 + 864 = 3114 cm³
    
    
    
18. The weight of a cuboidal metal box of dimensions 4.5 m × 4 m × 3 m is 12 kg. Find the weight of the box of dimensions 6 m × 2.5 m × 3 m of same metal.
    Solution:
    Volume of given box = 4.5 × 4 × 3 m³
    Weight of (4. 5 × 4 × 3) m³ metal box = 12 kg
    Then, weight of 1 m³ metal box
    Now, weight of (6 × 2.5 × 3) m³ metal box = 10 kg
    
    
19. The radius of following pillar is 14 cm and height is 6 m. It is painted with golden colour and cost of painting is Rs. 16 per m2. What can be the cost of painting 30 such pillars. (Use p = 22/7)
    
    Solution:
    Radius of pillar = 14 cm = 0.14 m
    Height of pillar = 6 m
    Curved surface area of cylinder 
    Now, cost of painting 30 such pillars = Rs. 30 × 5.28 = Rs. 158.40
    
    
20. Four small equal rectangles are cut off from each corner of a big rectangle. Find the area of portion left after removing them.
    
    
    Solution:
    Area of big rectangle = 20 × 10 = 200 cm2
    Length of each small rectangle= = 5 cm
    Breadth of each small rectangle= = 2.5 cm
    Area of each small rectangle = 5 × 2.5 = 12.5 cm²
    Then, area of four small rectangles = 4 × 12.5 = 50 cm²
    Therefore, required area = Area of big rectangle – Area of four small rectangles
    = 200 – 50 = 150 cm²