Advertisements
Advertisements
Question
Four cubes, each of edge 9 cm, are joined as shown below :
Write the dimensions of the resulting cuboid obtained. Also, find the total surface area and the volume
Solution
Edge of each cube = 9 cm
(i) Length of the cuboid fonned by 4 cubes (l) = 9 x 4 = 36 cm
Breadth (b) = 9 cm and height (h) = 9 cm
(ii) Total surface area of the cuboid = 2(lb + bh + hl)
= 2 (36 x 9 + 9 x 9 + 9 x 36) cm2
= 2 (324 + 81 + 324) cm2
= 2 x 729 cm2
= 1458 cm2
(iii) Volume = l x b x h = 36 x 9 x 9 cm2 = 2916 cm3
APPEARS IN
RELATED QUESTIONS
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the
flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.
A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 5 per metre sheet, sheet being 2 m wide.
Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?
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.
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 cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m × 1.5 m and 10 windows each of size 1.5 m × 1 m. If the cost of white-washing the walls of the hall at the rate of Rs 1.20 per m2 is Rs 2385.60, fidn the breadth of the hall.
Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.
The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the wall.
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m2 is Rs. 1248. Find the dimensions of the box.
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.
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`
The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall if each requires 150 m3 of air?
75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m3 of the air; find the height of the room.
Find the volume and the total surface area of a cuboid, whose :
l = 3.5 m, b = 2.6 m and h = 90 cm
Find the length of each edge of a cube, if its volume is :
(i) 216 cm3
(ii) 1.728 m3
The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.
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.
Three equal cubes of sides 5cm each are placed to form a cuboid. Find the volume and the total surface area of the cuboid.
375 persons can be accommodated in a room whose dimensions are in the ratio of 6 : 4 : 1. Calculate the area of the four walls of the room if the each person consumes 64m3 of air.
All six faces of a cuboid are ______ in shape and of ______ area.
A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.
