Advertisements
Advertisements
Question
A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?
Advertisements
Solution
Edge of a cube = 6 cm
Volume = a3 = (6)3 = 216 cm3
Dimensions of a cuboid = 4 cm x x cm x 15 cm
Volume = 60x cm3
The volume of both is equal
(i) ∴ `60x = 216 ⇒ x = 216/60 = 36/10`
∴ x = 3.6 cm
(ii) Total surface area of cuboid
= 2[lb + bh + hl]
= `2[4 xx 3.6 + 3.6 xx 15 + 15 xx 4]` cm2
= 2[14.4 + 54.0 + 60] cm2
= `128.4 xx 2 = 256.8` cm2
(iii) Total surface area of cube
= `6a^2 = 6(6)^2 = 6 xx 36 = 216` cm2
(iv) Difference of surface areas = 256.8 - 216
= 40.8 cm2
∴ Surface area of cuboid is greater
APPEARS IN
RELATED QUESTIONS
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost
of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.
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?
A tea-packet measures 10 cm × 6 cm × 4 cm. How many such tea-packets can be placed in a cardboard box of dimensions 50 cm × 30 cm × 0.2 m?
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
Find the surface area of a cuboid whose llength = 2 m, breadth = 4 m, height = 5 m .
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.
The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs 3.50 per square metre.
A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is
Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is
If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm2, find the length, the breadth and the height of the solid.
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.
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 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
Find the volume of wood required to make a closed box of external dimensions 80 cm, 75 cm, and 60 cm, the thickness of walls of the box being 2 cm throughout.
Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.
Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm2.
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.
An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?
The total surface area of a cuboid is 46m2. If its height is 1m and breadth 3m, find its length and volume.
Find the volume of wood used in making a closed box 22 cm by 18 cm by 14 cm, using a 1 cm thick wood. Also, find the cost of wood required to make the box at the rate of Rs. 5 per cm³ How many cubes of side 2 cm can be placed in the box?
The length of a cold storage is double its breadth. Its height is 3m. The area of its four walls including doors is 108m2. Find its volume.
