Advertisements
Advertisements
Question
A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick; find :
(i) the capacity of the box ;
(ii) the volume of metal-sheet and
(iii) weight of the box, if 1 cm3 of metal weighs 3.6 gm.
Solution
External length of the closed box = 66cm.
External breadth of the closed box = 36 cm
External height of the closed box =21 cm
External volume of the closed box= 66 x 36 x 21 = 49896 cm3
Internal length of the box =(66 – 2 x 0.5) = 66 – 1 = 65 cm
Internal breadth of the box =(36 – 2 x 0.5) = 36 – 1 = 35 cm
Internal height of the box = (21 – 2 x 0.5) = 21 – 1 = 20 cm
Internal Volume of the box = 65 x 35 x 20 = 45500 cm3
(i) Capacity of the box = 45500 cm3
(ii) Volume of metal sheet of the box = External volume – Internal volume
= 49896 – 45500 = 4396 cm3
(iii) 1 cm3 of metal weigh 3.6 grams.
Weight of the box = 4396 x 3.6 gm = 15825.6 gm
APPEARS IN
RELATED QUESTIONS
The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.
The cost of preparing the walls of a room 12 m long at the rate of Rs. 1.35 per square metre is Rs. 340.20 and the cost of matting the floor at 85 paise per square metre is Rs. 91.80. Find the height of the room.
Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.
The length , breadth and height of a room are 5 m, 4.5 m and 3 m, respectively. Find the volume of the air it contains.
How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and cement used in the construction is negligible?
A swimming pool is 20 m long 15 m wide and 3 m deep. Find the cost of repairing the floor and wall at the rate of Rs 25 per square metre.
The perimeter of a floor of a room is 30 m and its height is 3 m. Find the area of four walls of the room.
Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.
The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm, respectively. Find the cost of plastering at the rate of Rs 8 per square metre.
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 `sqrt(3)` cm. Find the edges of three cubes.
Find the edge of a cube whose surface area is 432 m2.
If the length of a diagonal of a cube is `8 sqrt(3)` cm, then its surface area is
Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is ______.
The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:
- The volume of the wood in the box;
- The cost of the box, if wood costs Rs. 1.20 per cm3;
- A number of 4 cm cubes that could be placed into the box.
The volume of a cuboid is 7.68 m3. If its length = 3.2 m and height = 1.0 m; find its breadth.
The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If the volume of the cuboid is 1.92 m3; find its length.
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
A solid cube of edge 14 cm is melted down and recast into smaller and equal cubes each of the edge 2 cm; find the number of smaller cubes obtained.
The dimension of a class-room are; length = 15 m, breadth = 12 m and height = 7.5 m. Find, how many children can be accommodated in this class-room; assuming 3.6 m3 of air is needed for each child.
A cylindrical pillar has a radius of 21 cm and a height of 4 m. Find:
- The curved surface area of the pillar.
- cost of polishing 36 such cylindrical pillars at the rate of ₹12 per m2.
If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5: 6, find the ratio of their curved surfaces.
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
The length breadth and height of a cuboid are in the ratio of 3 : 3 : 4. Find its volume in m3 if its diagonal is `5sqrt(34)"cm"`.
A room is 5m long, 2m broad and 4m high. Calculate the number of persons it can accommodate if each person needs 0.16m3 of air.
A metallic sheet is of the rectangular shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.
External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm2 is Rs 11,750, find the dimensions of the box.
