Advertisements
Advertisements
प्रश्न
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?
उत्तर
(i) Edge of cube = 10 cm
Length (l) of box = 12.5 cm
Breadth (b) of box = 10 cm
Height (h) of box = 8 cm
Lateral surface area of cubical box = 4(edge)2
= 4(10 cm)2
= 400 cm2
Lateral surface area of cuboidal box = 2[lh + bh]
= [2(12.5 × 8 + 10 × 8)] cm2
= (2 × 180) cm2
= 360 cm2
Clearly, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box.
Lateral surface area of cubical box − Lateral surface area of cuboidal box = 400 cm2 − 360 cm2 = 40 cm2
Therefore, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box by 40 cm2.
(ii) Total surface area of cubical box = 6(edge)2 = 6(10 cm)2 = 600 cm2
Total surface area of cuboidal box
= 2[lh + bh + lb]
= [2(12.5 × 8 + 10 × 8 + 12.5 × 10] cm2
= 610 cm2
Clearly, the total surface area of the cubical box is smaller than that of the cuboidal box.
Total surface area of cuboidal box − Total surface area of cubical box = 610 cm2 − 600 cm2 = 10 cm2
Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm2.
APPEARS IN
संबंधित प्रश्न
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.
How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
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?
Find the surface area of a cuboid whoselength = 3.2 m, breadth = 30 dm, height = 250 cm.
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.
Find the volume and the total surface area of a cuboid, whose :
length = 15 cm, breadth = 10 cm and height = 8 cm.
The dining-hall of a hotel is 75 m long; 60 m broad and 16 m high. It has five – doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of Rs.12 per m2;
(ii) carpetting its floor at the rate of Rs.25 per m2.
Find the area of metal-sheet required to make an open tank of length = 10 m, breadth = 7.5 m and depth = 3.8 m.
Three identical cubes of side 4 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid
The surface area of a cuboid formed by joining two cubes of side a face to face is ______.
