Recent questions tagged mensuration

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Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...
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Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...
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A solid right circular cone of height $27$ cm is cut into two pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume ...
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A man makes complete use of $405$ cc of iron, $783$ cc of aluminium, and $351$ cc of copper to make a number of solid right circular cylinders of each type of metal. Thes...
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The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyram...
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A right circular cone, of height $12$ ft, stands on its base which has diameter $8$ ft. The tip of the cone is cut off with a plane which is parallel to the base and $9$ ...
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A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1:8: 27: 27$. The percentage by which the sum of the surface areas of these fi...
A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9\pi \;\text{cm}^{3}$. Then ...
A cube of side $12\; \text{cm}$ is painted red on all the faces and then cut into smaller cubes, each of side $3 \text{cm}$. What is the total number of smaller cubes hav...
A wooden box (open at the top) of thickness $0.5\:\text{cm}$, length $21\:\text{cm}$, width $11\:\text{cm}$ and height $6\:\text{cm}$ is painted on the inside. The expens...
A wooden box (open at the top) of thickness $0.5$ cm, length $21$ cm, width $11$ cm and height $6$ cm is painted on the inside. The expenses of painting are $\text{Rs. 70... 1 answer 12 If the rectangular faces of a brick have their diagonals in the ratio$3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of i... 1 answer 13 A cuboidal aquarium, of base dimensions$100\;\text{cm} \times 80\;\text{cm}$and height$60\;\text{cm}$, is filled with water to its brim. The aquarium is now tilted alo... 0 answers 14 A solid sphere of radius$12$inches and cast into a right circular cone whose base diameter is$\sqrt{2}$times its slant height. If the radius of the sphere and the cone... 0 answers 15 Consider a cylinder of height h cms and radius$r=\frac{2}{\pi}$cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindri... 0 answers 16 Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds$500$litres more than the conical tank. After$200$li... 0 answers 17 There are$8436$steel balls, each with a radius of$1$centimeter, stacked in a pile, with$1$ball on top,$3$balls in second layer,$6$in the third layer,$10$in th... 1 answer 18 Let$\text{A}$and$\text{B}$two solid spheres such that the surface area of$\text{B}$is$300\%$higher than the surface area of$\text{A}.$The volume of$\text{A}$i... 0 answers 19 A lead cuboid of$8$inches in length,$11$inches in breadth, and$2$inches thick was melted and resolidified into the form of a rod of$8$inches diameter. The length ... 0 answers 20 Three identical cones with base radius$r$are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is smal... 2 answers 21 If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribi... 1 answer 22 The length, breadth and height of a room are in the ration$3:2:1.$If the breadth and height are halved while the length is doubled, then the total area of the four wall... 0 answers 23 Consider a right circular cone of base radius$4$cm and height$10\$ cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of t...