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Surface Areas and Volume of Solids MATHEMATICS - Surface Areas and Volume of Solids

ICSE - STD 9 - MATHEMATICS (ICSE - English Medium). 79 questions in this chapter.

Question types

Surface Areas and Volume of Solids question types

79 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.

79
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4
Question groups
5
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Sample Questions

Surface Areas and Volume of Solids questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1[2 Mark Question Answer]2 Marks
$\text{ABCDE}$ is the end view of a factory shed which is $50\  m$ long. The roofing of the shed consists of asbestos sheets as shown in the figure. The two ends of the shed are completely closed by brick walls.
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Find the total surface area $($including roofing$)$ of the shed.
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Q 3[3 marks sum]3 Marks
The cross section of a tunnel perpendicular to its length is a trapezium $\text{ABCD}$ as shown in the figure. $A M=B N ; A B=4.4 m, C D=3 m$ The height of a tunnel is $2.4 \ m$ . The tunnel is $5.4 \ m$ long. Calculate the cost of flooring at the rate of $Rs. 2.5$ per $m ^2$.
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Q 4[3 marks sum]3 Marks
The figure shows the cross section of $0.2\ m$ a concrete wall to be constructed. It is $0.2\ m$ wide at the top, $2.0\ m$ wide at the bottom and its height is $4.0\ m$, and its length is $40\ m$. Calculate the volume of the concrete in the wall
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Q 5[3 marks sum]3 Marks
Rain falls on a rectangular roof $28\ m$ by $9\ m$ and the water flows into a tank of dimensions $90\ m$ by $70 \ cm$ by $84 \ cm$. How much rainfall will fill the tank completely?
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Q 6[3 marks sum]3 Marks
The figure represents the cross section of a swimming pool $10\ m$ broad, $2\ m$ deep at one end, $3\ m$ deep at the other end. Calculate the volume of water it will hold when full, given that its length is $40\ m.$
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Q 7[3 marks sum]3 Marks
How many liters of water will flow out of a pipe having a cross sectional area $6 \ cm^2$ in one hour, if the speed of water in the pipe is $30 \ cm/sec$?
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Q 8[4 marks sum]4 Marks
The area of cross section of a pipe is $5.4$ square / cm and water is pumped out of it at the rate of $27\ km$ per hour. Find, in litres, the volume of water which flows out of the pipe in $2$ minutes.
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Q 9[4 marks sum]4 Marks
A swimming pool is $50\ m$ long and $15\ m$ wide. Its shallow and deep ends are $1.5\ m$ and $4.5\ m$ respectively. If the bottom of the pool slopes uniformly, find the amount of water in kilolitres required to fill the pool $(1\ m^3 = 1000$ liters$).$
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Q 10[4 marks sum]4 Marks
Water flows at the rate of $1.5$ meters per second through a pipe with area of cross section $2.5 \ cm 2$ into a rectangular water tank of length $90 \ cm$ and breadth $50 \ cm$. Find the rise in water level in the tank after $4$ minutes.
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Q 11[4 marks sum]4 Marks
The given figure is a cross $-$section of a victory stand used in sports. All measurements are in centimetres. Assume all angles in the figure are right angles. If the width of the stand is $60 \ cm$ , find The total surface area in $m ^2$.
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Q 12[4 marks sum]4 Marks
A rectangular water tank measuring $8\ m \times 6\ m \times 4 \ cm$ is filled from a pipe of cross sectional area $1.5 \ cm^2$, the water emerging at $10\ m/s$. How long does it take to fill the tank?
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Q 13[5 marks sum]5 Marks
The cross section of a tunnel perpendicular to its length is a trapezium $\text{ABCD}$ as shown in the figure. $AM = BN; AB = 4.4\ m, CD = 3\ m$ The height of a tunnel is $2.4\ m$. The tunnel is $5.4\ m$ long.Calculate the cost of painting the internal surface of the tunnel $($excluding the floor$)$ at the rate of $Rs. 5$ per $m^2$.
Image
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Q 14[5 marks sum]5 Marks
The figure shows the cross section of $0.2\ m$ a concrete wall to be constructed. It is $0.2\ m$ wide at the top,$ 2.0\ m$ wide at the bottom and its height is $4.0\ m$, and its length is $40\ m.$ If the whole wall is to be painted, find the cost of painting it at $2.50$ per sq $m.$
Image
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Q 15[5 marks sum]5 Marks
The figure shows the cross section of $0.2\ m$ a concrete wall to be constructed. It is $0.2\ m$ wide at the top, $2.0\ m$ wide at the bottom and its height is $4.0\ m$, and its length is $40\ m$. Calculate the cross sectional area
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Q 16[5 marks sum]5 Marks
The given figure is a cross$-$section of a victory stand used in sports. All measurements are in centimetres. Assume all angles in the figure are right angles. If the width of the stand is $60 \ cm$, find The space it occupies in $cm^3.$
Image
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