CBSE Class 10 Maths (Basic) 2025 · Paper 430/6/1 · Question 37

Surface Areas and Volumes 4 marks Medium

A hemispherical bowl is packed in a cuboidal box. The bowl just fits in the box. Inner radius of the bowl is

10

cm. Outer radius of the bowl is

10.5

cm. Based on the above, answer the following questions.

Bowl inside cuboidal box

iFind the dimensions of the cuboidal box.[1]
iiFind the total outer surface area of the box.[1]
iii(a)Find the difference between the capacity of the bowl and the volume of the box. (use $π = 3.14$ )[2]
iii(b)The inner surface of the bowl and the thickness is to be painted. Find the area to be painted.[2]

Answer

(i) Length

21

cm, breadth

21

cm, height

10.5

cm; (ii) Total outer surface area

= 1764

cm²; (iii)(a) Difference

= \frac{15223}{6} \approx 2537.17

cm³; (iii)(b) Area to be painted

= 210.25 π

cm², which is

\frac{9251}{14} \approx 660.79

cm² with

π = \frac{22}{7}

(or

\approx 660.19

cm² with

π = 3.14

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