Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
\[\text { The dimensions of the three cuboids are 5 cm }\times 6 cm \times 7 cm, 4 cm \times 7 cm \times 8 cm \text { and } 2 cm \times 3 cm \times 13 cm . \]
\[\text { Now, a new cube is formed by melting the given cuboids }. \]
\[ \therefore \text { Voulume of the cube = sum of the volumes of the cuboids }\]
\[ = (5 cm \times 6 cm \times 7 cm) + (4 cm \times 7 cm \times 8 cm) + (2 cm \times 3 cm \times 13 cm)\]
\[ = (210 {cm}^3 ) + (224 {cm}^3 ) + (78 {cm}^3 )\]
\[ = 512 {cm}^3 \]
\[\text { Since volume of a cube = (side ) }^3 , \text { we have }: \]
\[512 =\text { (side ) }^3 \]
\[ \Rightarrow (\text { side) } = \sqrt[3]{512} = 8 cm\]
\[ \therefore \text { The side of the new cube is 8 cm } .\]
APPEARS IN
संबंधित 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?
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.
Hameed has built a cubical water tank with lid for his house, with each other edge 1 .5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
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.
A swimming pool is 20 m long 15 m wide and 3 m deep. Find the cost of repairing the floor and wall at the rate of Rs 25 per square metre.
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.
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
