The dimensions of a car petrol tank are $50 \ cm \times 32 \ cm \times 24 \ cm,$ which is full of petrol. If a car's average consumption is $15 \ km$ per liter, find the maximum distance that can be covered by the car.
View full solution →Question types
Solids [Surface Area and Volume of 3-D Solids] question types
45 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
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Sample Questions
Solids [Surface Area and Volume of 3-D Solids] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A rectangular field is $112 \ m$ long and $62 \ m$ broad. A cubical tank of edge $6 \ m$ is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.
View full solution →The internal dimensions of a rectangular box are $12 \ cm \times 9 \ cm$ . If the length of the longest rod that can be placed in this box is $17 \ cm$; find $x$.
View full solution →Water is discharged from a pipe of a cross-section area $3.2 \ cm^2$ at the speed of $5 m / s$. Calculate the volume of water discharge $:(i) In \ cm ^3 $ per sec .$(ii)$ In liters per minute.
View full solution →The following figure shows a solid of uniform cross$-$section. Find the volume of the solid. All measurements are in centimeters.
Assume that all angles in the figures are right angles.
View full solution →Assume that all angles in the figures are right angles.
A school auditorium is $40 \ m$ long, $30 \ m$ broad and $12 \ m$ high. If each student requires $1.2 m^2$ of the floor area; find the maximum number of students that can be accommodated in this auditorium. Also, find the volume of air available in the auditorium, for each student.
View full solution →Each face of a cube has a perimeter equal to $32 \ cm$. Find its surface area and its volume.
View full solution →A swimming pool is $18\ m$ long and $8\ m$ wide. Its deep and shallow ends are $2\ m$ and $1.2\ m$ respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly.
View full solution →A hose-pipe of cross-section area $2\ cm^2$ delivers $1500$ liters of water in $5$ minutes. What is the speed of water in $m/s$ through the pipe?
View full solution →A swimming pool is $40 \ m$ long and $15 \ m$ wide. Its shallow and deep ends are $1.5 \ m$ and $3 \ m$ deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in liters required to fill the pool.
View full solution →The dimensions of a solid metallic cuboid are $72 \ cm \times 30 \ cm \times 75 \ cm$. It is melted and recast into identical solid metal cubes with each edge $6 \ cm$. Find the number of cubes formed.Also, find the cost of polishing the surfaces of all the cubes formed at the rate $Rs. 150$ per $sq. m.$
View full solution →The dimensions of a rectangular box are in the ratio $4: 2 : 3$. The difference between the cost of covering it with paper at $Rs. 12 \sim$per$ \sim m^2$ and with paper at the rate of $13.50 \sim$per $\sim m^2$ is $Rs. 1,248$. Find the dimensions of the box.
View full solution →A rectangular cardboard sheet has length $32\ cm$ and breadth $26\ cm$. Squares each of side $3\ cm$, are cut from the corners of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.
View full solution →A rectangular water$-$tank measuring $80 \ cm \times 60\ cm$ is filled form a pipe of cross$-$sectional area $1.5 \ cm^2$, the water emerging at $3.2 m/s$. How long does it take to fill the tank?
View full solution →A hollow square$-$shaped tube open at both ends is made of iron. The internal square is of $5 \ cm$ side and the length of the tube is $8 \ cm$. There are $192 ~cm^3$ of iron in this tube. Find its thickness.
View full solution →A rectangular tank $30 \ cm \times 20 \ cm \times 12 \ cm$ contains water to a depth of $6 \ cm$ . A metal cube of side $10 \ cm$ is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in liters, that must be poured in the tank so that the metal cube is just submerged in the water.
View full solution →When the length of each side of a cube is increased by $3 \ cm$, its volume is increased by $2457 \ cm^3$. Find its side. How much will its volume decrease, if the length of each side of it is reduced by $20\%$?
View full solution →The internal length, breadth, and height of a box are $30 \ cm, 24 \ cm$, and $15 \ cm$. Find the largest number of cubes which can be placed inside this box if the edge of each cube is$;(i) 3 \ cm ;(ii) 4 \ cm ;(iii) 5 \ cm$
View full solution →The cross-section of a piece of metal $4$ m in length is shown below. Calculate :
$(i)$ The area of the cross$-$section;$(ii)$ The volume of the piece of metal in cubic centimeters.If $1$ cubic centimeter of the metal weighs $6.6\ g$, calculate the weight of the piece of metal to the nearest $kg.$
View full solution →$(i)$ The area of the cross$-$section;$(ii)$ The volume of the piece of metal in cubic centimeters.If $1$ cubic centimeter of the metal weighs $6.6\ g$, calculate the weight of the piece of metal to the nearest $kg.$
The cross-section of a tunnel perpendicular to its length is a trapezium $\text{ABCD}$ as shown in the following figure; also given that:$A M=B N ; A B=7 m ; C D=5 m$. The height of the tunnel is $2.4 m $. The tunnel is $40 m$ long. Calculate:
$(i)$ The cost of painting the internal surface of the tunnel $($excluding the floor$)$ at the rate of $Rs. 5$ per $m^2 ($sq. meter$).(ii)$ The cost of paving the floor at the rate of $Rs.18$ per $m^2.$
View full solution →$(i)$ The cost of painting the internal surface of the tunnel $($excluding the floor$)$ at the rate of $Rs. 5$ per $m^2 ($sq. meter$).(ii)$ The cost of paving the floor at the rate of $Rs.18$ per $m^2.$
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