Sample QuestionsSurface Areas and Volumes questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Write True or False and justify your answer in the following: If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
Write True or False and justify your answer in the following: A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
Write True or False and justify your answer in the following: If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be $6:\pi.$
View full solution →Write True or False and justify your answer in the following: The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ equals to the volume of a hemisphere of radius $r.$
View full solution →Write True or False and justify your answer in the following:
If the length of the diagonal of a cube is $6\sqrt{3}\text{cm},$ then the length of the edge of the cube is $3\ cm$
View full solution →A shopkeeper has one spherical laddoo of radius $5\ cm$. With the same amount of material, how many laddoos of radius $2.5\ cm$ can be made?
View full solution →How many square metres of canvas is required for a conical tent whose height is $3.5\ m$ and the radius of the base is $12\ m?$
View full solution →Metal spheres, each of radius $2\ cm$, are packed into a rectangular box of internal dimensions $16cm \times 8cm \times 8cm.$ When $16$ spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[\text{Use }\pi=3.14]$
View full solution →A school provides milk to the students daily in a cylindrical glasses of diameter $7\ cm$. If the glass is filled with milk upto an height of $12\ cm$, find how many litres of milk is needed to serve $1600$ students.
View full solution →A cylindrical roller $2.5m$ in length, $1.75m$ in radius when rolled on a road was found to cover the area of $5500m^2$. How many revolutions did it make?
View full solution →A right triangle with sides $6\ cm, 8\ cm$ and $10\ cm$ is revolved about the side $8\ cm$. Find the volume and the curved surface of the solid so formed.
View full solution →A small village, having a population of $5000$ , requires $75$ litres of water per head per day. The village has got an overhead tank of measurement $40 m \times 25 \ m \times 15 \ m$. For how many days will the water of this tank last?
View full solution →The volumes of the two spheres are in the ratio $64 : 27$. Find the ratio of their surface areas.
View full solution →A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height$?$
View full solution →A cloth having an area of $165\ m^2$ is shaped into the form of a conical tent of radius $5\ m$
$i.$ How many students can sit in the tent if a student, on an average, occupies $\frac{5}{7}\text{m}^2$ on the ground?
$ii.$ Find the volume of the cone.
View full solution →Two solid spheres made of the same metal have weights $5920g$ and $740g$, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is $5\ cm.$
View full solution →The water for a factory is stored in a hemispherical tank whose internal diameter is $14\ m$. The tank contains $50$ kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
View full solution →A cylindrical tube opened at both the ends is made of iron sheet which is $2\ cm$ thick. If the outer diameter is $16\ cm$ and its length is $100\ cm$, find how many cubic centimeters of iron has been used in making the tube?
View full solution →$30$ circular plates, each of radius $14\ cm$ and thickness $3\ cm$ are placed one above the another to form a cylindrical solid. Find:
$i.$ The total surface area.
$ii.$ Volume of the cylinder so formed.
View full solution →A semi-circular sheet of metal of diameter $28cm$ is bent to form an open conical cup. Find the capacity of the cup.
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