MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

Case Study 3: A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled. The diameter of spherical ball is 21 cm. Cylindrical pool - Outer diameter is 50 cm and inner diameter is 40 cm. Height of solid base is 14 cm. Height of water filled is 7 cm. Observe the figure and answer the following questions :

(i)
Determine the total height of the fountain.
1 mark
(ii)
Find the volume of the ball.
1 mark
(iii)(a)
If one-third of the ball is submerged in the water, find the volume of the water filled in the pool.
2 marks
OR
(iii)(b)
Find the sum of the outer curved surface area of the cylindrical part and surface area of the ball.
2 marks

Figure in the paper: Photograph of a leafy spherical ball resting in a cylindrical pool. Side diagram: sphere sitting in a cylindrical pool; water level marked 7 cm above the solid base; solid base height marked 14 cm; the ball partially immersed in the water. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

The ball sits on the 14 cm base, so add its diameter to the base height.

Hint 2

Use $\frac{4}{3} π r^{3}$ with r = 10.5 cm. For the water, take the inner cylinder of radius 20 cm and height 7 cm.

Hint 3

Subtract the part of the ball under water. For (iii)(b), the outer cylinder has radius 25 cm and height 14 + 7 cm; add $4 π r^{2}$ for the ball.

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.

(i) The ball rests on top of the solid base. Total height = height of base + diameter of ball:
$14 + 21 = 35 cm$
1 mark
(ii) Radius of ball $r = \frac{21}{2}$ cm.
$V = \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$
½ mark
(ii) $V = 4851 cm^{3}$
½ mark
(iii)(a) The inner radius of the pool is $20$ cm and the water height is $7$ cm. One-third of the ball's volume lies in this space.
Volume of water = inner cylinder volume − $\frac{1}{3}$ of ball volume
$= \frac{22}{7} \times 20 \times 20 \times 7 - \frac{1}{3} \times 4851$
1 mark
(iii)(a) $= 8800 - 1617 = 7183 cm^{3}$
1 mark
(iii)(b) The outer radius is $25$ cm and the outer height of the cylindrical part is $14 + 7 = 21$ cm.
Required area = $2 π R h + 4 π r^{2}$
$= 2 \times \frac{22}{7} \times 25 \times 21 + 4 \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}$
1 mark
(iii)(b) $= 3300 + 1386 = 4686 cm^{2}$
1 mark

Answer: (i) 35 cm; (ii) 4851 cm³; (iii)(a) 7183 cm³; (iii)(b) 4686 cm²

Where the marks are

(i) Total height $14 + 21 = 35$ cm (1 mark)
(ii) Correct substitution in $\frac{4}{3} π r^{3}$ (½ mark) and gets 4851 cm³ (½ mark)
(iii)(a) Inner cylinder volume minus one-third of ball volume, correctly substituted (1 mark)
(iii)(a) Gets 7183 cm³ (1 mark)
(iii)(b) Correct expression $2 π \times 25 \times 21 + 4 π (10.5)^{2}$ (1 mark)
(iii)(b) Gets 4686 cm² (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area and Volume Formulae Revision

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 paper2026 board paper, set 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 38

Hints

Step-by-step solution

Revise the chapter

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