Practice-Questions-Surface-Area-and-Volume - Part 1 - Cube, Cuboid, Cylinder

Sep 18, 2026

Uploaded by Eden

MATHEMATICS revision exercises focused on mensuration, specifically surface area and volume topics covering cube, cuboid, cylinder, and related composite solids. The practice set includes problem types on rhombus perimeter from diagonals, areas of quadrilaterals and fields using given dimensions, shaded-region area, and conversions between volume and dimensions for storage and containers. It also emphasizes scaling effects on volume when edges or dimensions change and includes real-world contexts such as garden cost and calculating material quantity or weight from density.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

Revision Exercise

Surface Area and Volume (Cube, Cuboid, Cylinder)

Mensuration Problem Set

Scaling and Applications

MATHEMATICS REVISION EXERCISE_041223 (Mensuration/ Surface Area and Volume: Cube, Cuboid, Cylinder) 1. If the area of a rhombus be 24 cm2 and one of its diagonals be 4 cm, find the perimeter of the rhombus. 2. Mrs. Kaushik has a square plot as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house, if cost of developing a garden is Rs 55 per square metre. 3. Find the area of the shaded region. 4. In quadrilateral ABCD shown in Figure, AB is parallel to DC and AD is perpendicular to AB. Also, AB = 8m, DC= BC = 5m. Find the area of the quadrilateral. 5. A field in the form of a parallelogram has one of its diagonals 42 m long and the perpendicular distance of this diagonal from either of the outlying vertices is 10.8 m (see Figure) . Find the area of the field. 6. Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively. 7. A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid? 8. The volume of a cylinder is 448 π cm3 and height 7 cm. Find its lateral surface area and total surface area. 9. A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk? 10. What will happen to the volume of a cube, if its edge is: (i) Halved? (ii) trebled? 11. What will happen to the volume of a cuboid if its : (i) Length is doubled, height is same and breadth is halved? (ii) Length is doubled, height is doubled and breadth is same? 12. Three cuboids of dimensions 5 cm x 6 cm x 7 cm, 4 cm x 7 cm x 8 cm and 2 cm x 3 cm x 13 cm melted and a cube is made. Find the side of cube. 13. The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder, assuming it is open at either end. 14. Find the weight of solid rectangular iron piece of size 50 cm x 40 cm x 10 cm, if 1 cm 3 of iron weighs 8 gm. 15. How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage? 16. A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, beads of volume 1.5 cm3 each are to be made. Find the number of beads that can be made from the block. 17. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 c.c. of iron weighs 8 gm. 18. Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm. 19. A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage. 20. A cube A has side thrice as long as that of cube B. What is the ratio of the volume of cube A to that of cube B? ANSWERS: 1. 8√10 􀜿􀝉 2. Rs. 17875 3. 30.5 cm2 4. 26 m2 5. 453.5 m2 6. 5 cm 7. 6 cm 8. LSA = 352 cm2; TSA = 754.28 cm2 9. 10 cm 10. (i) 1/8 times; (ii) 27 times 11. (i) same; (ii) 4 times 12. 8 cm 13. 160 kg 14. 5270 cm3 15. 72 16. 84 17. 1424.3 Kg 18. 576 19. 2550 20. 27:1

FAQs

Which solid shapes and mensuration topics are covered in these practice questions?

The questions focus on cube, cuboid, and cylinder, along with related surface area and volume calculations and mensuration-based area problems.

How do the questions assess the effect of changing a cube or cuboid’s dimensions?

They ask what happens to volume when the cube’s edge is halved or trebled and when cuboid dimensions are doubled/halved in specified combinations.

What types of real-world application problems are included?

There are application questions like finding garden development cost based on area, determining container dimensions to hold a given volume of liquid, and calculating material weight or number of blocks from given dimensions.

Sep 18, 2026

Uploaded by Eden