15 Questions
What is the total cost of white washing the four walls of a room with dimensions 12m x 8m x 4m at a cost of `5 per m2?
`1280
What is the cost of painting the curved surface area of 24 cylindrical pillars, each with a radius of 28cm and height of 4m, at a rate of `8 per m2?
`1351.68
If a cylinder has a radius of 7cm and a total surface area of 968 cm2, what is its height?
15 cm
How many meters of tarpaulin of width 96 cm is required to cover 100 suitcases with measures 80 cm × 48 cm × 24 cm each?
200 m
Find the side length of a cube with a surface area of 600 cm^2.
10 cm
If Rukhsar painted all except the bottom of a cabinet with measures 1 m × 2 m × 1.5 m, how much surface area did she cover?
9 m^2
How many cans of paint will Daniel need to paint the walls and ceiling of a hall with dimensions 15 m × 10 m × 7 m if each can covers 100 m^2?
10 cans
Which box has a larger lateral surface area, a cuboidal box with measures 80 cm × 48 cm × 24 cm or a cube with a side length of 10 cm?
Cuboidal box
How much sheet of metal is required to make a closed cylindrical tank with a radius of 7 m and height of 3 m?
188 m^2
What are the length, width, and height of a cube?
The length, width, and height of a cube are all equal.
What is the total surface area of a cube?
The total surface area of a cube is 6 times the area of one face.
If each side of a cube is l, what is the area of each face?
The area of each face of a cube with side length l is $l^2$.
How can you arrange 12 cubes of equal length to form a cuboid with the smallest surface area?
Arrange the 12 cubes into a cuboid with dimensions 3 by 2 by 2.
After painting the surface of a cube and cutting it into 64 smaller cubes, how many have no face painted?
8 smaller cubes have no face painted.
What is the surface area of a cuboid formed by joining two cubes, each with a side length of b?
The surface area of the cuboid formed by joining two cubes is 10b².
Study Notes
Surface Areas and Volumes
- A suitcase with measures 80 cm × 48 cm × 24 cm requires a tarpaulin cloth of width 96 cm to cover it.
- 100 suitcases require 80 metres of tarpaulin.
Cubes
- A cube has a surface area of 600 cm², with each side being √(600/6) = 10 cm.
- A cube has a lateral surface area equal to the area of one face multiplied by 4.
Painting Surfaces
- Rukhsar painted the outside of a cabinet of measure 1 m × 2 m × 1.5 m, covering all except the bottom, for a total surface area of 13 m².
- Daniel needs to paint a cuboidal hall with length, breadth, and height of 15 m, 10 m, and 7 m respectively, requiring 100 m² of area per can of paint.
Cylinders
- A closed cylindrical tank of radius 7 m and height 3 m requires a metal sheet of 470.4 m² to cover it.
- A cylindrical container with a diameter of 14 cm and height 20 cm, when its surface is labelled, requires an area of 2πrh = 880 cm².
Road Roller
- A road roller takes 750 complete revolutions to move once over to level a road, covering an area of 2475.44 m².
Cylindrical Pillars
- 24 cylindrical pillars, each with a radius of 28 cm and height of 4 m, have a total curved surface area of 168.96 m², costing
1351.68 to paint at8 per m².
Height of a Cylinder
- A cylinder with a radius of 7 cm and total surface area of 968 cm² has a height of 15 cm.
Cubes and Cuboids
- A cube has equal length, width, and height, and each face is a square.
- The area of each face of a cube is equal, and the total surface area is 6l², where l is the side of the cube.
- Two cubes joined to form a cuboid have a surface area of 10b².
- 12 cubes of equal length arranged to form a cuboid of smallest surface area have a surface area of 10b².
This quiz presents geometry and measurement problems involving calculating the amount of material required to cover boxes, finding surface areas of cubes, and determining the amount of surface area covered when painting specific dimensions. Test your geometry and measurement skills with these practical problems.
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