MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 34(a)

From the official CBSE sample question paper for 2023-24, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerCompetency-basedSurface Areas and Volumes

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? What should be the speed of water if the rise in water level is to be attained in 1 hour?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

The water that enters the pond is a cuboid 50 m × 44 m × 0.21 m.

Hint 2

In one hour the water from the pipe forms a cylinder of radius 0.07 m and length 15000 m.

Hint 3

Divide the pond volume by the volume delivered per hour. For a 1-hour fill, ask how long the water cylinder must be.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Volume of water needed in the pond $= l \times b \times h$ , with $h = 21$ cm $= \frac{21}{100}$ m:
$V = 50 \times 44 \times \frac{21}{100} = 462 m^{3}$
1 mark
Radius of the pipe $r = \frac{14}{2} = 7$ cm $= \frac{7}{100}$ m.
Area of cross-section $= π r^{2} = \frac{22}{7} \times \frac{7}{100} \times \frac{7}{100} = \frac{154}{10000} m^{2}$
1 mark
Speed of flow $= 15$ km/h $= 15000$ m/h. In 1 hour a column of water 15000 m long leaves the pipe.
Volume flowing in 1 hour $= \frac{154}{10000} \times 15000 = 231 m^{3}$
1 mark
Time required $= \frac{volume of pond water}{volume per hour} = \frac{462}{231} = 2$ hours
1 mark
To fill $462 m^{3}$ in 1 hour, the length of the water column per hour must be $\frac{462}{154/10000} = 30000$ m.
So the speed must be 30000 m/h $= 30$ km/h. (Doubling the speed halves the time.)
1 mark

Answer: 2 hours; required speed = 30 km/h

Where the marks are

Volume of the pond's water $= 462 m^{3}$ (1 mark)
Cross-section area of the pipe $= \frac{154}{10000} m^{2}$ (1 mark)
Converts 15 km/h to 15000 m/h and finds the volume per hour (1 mark)
Time = 2 hours (1 mark)
Speed for 1 hour = 30 km/h (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Cube, Cuboid and Cylinder Combination Problems

Practise this chapterBoard-style questions from Surface Areas and Volumes, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2023-24: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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