Advertisements
Advertisements
प्रश्न
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
उत्तर
\[\text { Length of the room = 12 }m\]
\[\text { Breadth = 9 m } \]
\[\text { Height = 8 m }\]
\[\text { Since the room is cuboidal in shape, the length of the longest rod that can be placed in the room will be equal to the length of the diagonal between opposite vertices }. \]
\[\text { Length of the diagonal of the floor using the Pythagorus theorem }\]
\[ = \sqrt{l^2 + b^2}\]
\[ = \sqrt{(12 )^2 + (9 )^2}\]
\[=\sqrt{144 + 81}\]
\[=\sqrt{225}\]
\[ = 15 m\]
\[\text { i . e . , the length of the longest rod would be equal to the length of the diagonal of the right angle triangle of base 15 m and altitude 8 m . } \]
\[\text { Similarly, using the Pythagorus theorem, length of the diagona l}\]
\[ = \sqrt{{15}^2 + 8^2}\]
\[=\sqrt{225 + 64}\]
\[ = 17 m\]
\[ \therefore \text { The length of the longest rod that can be placed in the room is 17 m }.\]
संबंधित प्रश्न
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?
How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?
A solid rectangular piece of iron measures 6 m by 6 cm by 2 cm. Find the weight of this piece, if 1 cm3 of iron weighs 8 gm.
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 volume of a cuboid is 3456 cm3. If its length = 24 cm and breadth = 18 cm ; find its height.
Find the volume and total surface area of a cube whose each edge is:
(i) 8 cm
(ii) 2 m 40 cm.
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm3, find its length.
A square plate of side 'x' cm is 4 mm thick. If its volume is 1440 cm3; find the value of 'x'.
Below are the drawings of cross sections of two different pipes used to fill swimming pools. Figure A is a combination of 2 pipes each having a radius of 8 cm. Figure B is a pipe having a radius of 15 cm. If the force of the flow of water coming out of the pipes is the same in both the cases, which will fill the swimming pool faster?
