CBSE Class 10 Maths (Basic) 2025 · Paper 430/4/1 · Question 37

Surface Areas and Volumes 4 marks Medium

Playing in a ball pool is good entertainment for kids. Suhana bought

600

new balls of diameter

7

cm to fill in the pool for her kids. The cuboidal box containing

600

balls has dimensions

42 cm \times 91 cm \times 50 cm

(l \times b \times h)

. Based on above information, answer the following questions :

(i)Find the volume of one ball.[1]
(ii)10 balls are painted with neon colours. Determine the area of painted surface.[1]
(iii)(a)Find the volume of empty space in the box.[2]
(iii)(b)OR : The lowermost layer of the balls covers the base of the box edge to edge when balls are placed evenly adjacent to each other. (A) How much area is covered by one ball? (B) How many balls are there in lowermost layer?[2]

Answer

(i) Volume of one ball

= \frac{539}{3} cm^{3} \approx 179.67 cm^{3}

; (ii) Area of painted surface

= 1540 cm^{2}

; (iii)(a) Volume of empty space

= 83300 cm^{3}

OR (iii)(b) (A) Area covered by one ball

= 49 cm^{2}

, (B) Number of balls in the lowermost layer

= 78

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