Advertisements
Advertisements
Question
Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.
Advertisements
Solution
\[\text { Length of the room = 12 }m\]
\[\text { Breadth = 9 m } \]
\[\text { Height = 8 m }\]
\[\text { Since the room is cuboidal in shape, the length of the longest rod that can be placed in the room will be equal to the length of the diagonal between opposite vertices }. \]
\[\text { Length of the diagonal of the floor using the Pythagorus theorem }\]
\[ = \sqrt{l^2 + b^2}\]
\[ = \sqrt{(12 )^2 + (9 )^2}\]
\[=\sqrt{144 + 81}\]
\[=\sqrt{225}\]
\[ = 15 m\]
\[\text { i . e . , the length of the longest rod would be equal to the length of the diagonal of the right angle triangle of base 15 m and altitude 8 m . } \]
\[\text { Similarly, using the Pythagorus theorem, length of the diagona l}\]
\[ = \sqrt{{15}^2 + 8^2}\]
\[=\sqrt{225 + 64}\]
\[ = 17 m\]
\[ \therefore \text { The length of the longest rod that can be placed in the room is 17 m }.\]
RELATED QUESTIONS
Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.
Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.
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 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.
A tank open at the top is made of iron sheet 4 m wide. If the dimensions of the tank are 12 m × 8 m × 6 m, find the cost of iron sheet at Rs 17.50 per metre.
The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm2, find its length.
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, 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.
In a building, there are 24 cylindrical pillars. For each pillar, the radius is 28 m, and the height is 4 m. Find the total cost of painting the curved surface area of the pillars at the rate of ₹ 8 per m2.
Find the capacity of water tank, in litres, whose dimensions are 4.2 m, 3 m and 1.8 m?
