Advertisements
Advertisements
प्रश्न
Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.
उत्तर
We have,
Edges of the cubes : a1 = 3 cm, a2 = 4 cm and a3 = 5 cm
Let the edge of the new cube be a.
Now,
` "Volume of the new cube" = a_1^3 +a_2^3+a_3^3`
`=>a^3 = 3^3 + 4^3 + 5^3`
⇒ a3 = 27 + 64 + 125
⇒ a3 = 216
`⇒ a = root(3)(216)`
∴ a = 6 cm
So, the edge of the new cube so formed is 6 cm.
APPEARS IN
संबंधित प्रश्न
A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that the mass of 1 cm3of iron is 8 gm.
The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.
A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe at the rate of \[3\frac{4}{7}\] litre per second. How much time will it take to make the tank half empty?\[\left[ Use \pi = \frac{22}{7} \right]\]
A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9` cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.
Choose the correct answer of the following question:
A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is
On increasing the radii of the base and the height of a cone by 20%, its volume will increase by
The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If their heights are in the ratio 2 : 3, the ratio between their volumes is
Find the perimeter and area of the shaded portion of the following diagram; give your answer correct to 3 significant figures. (Take π = 22/7).
