CBSE Class 10 Maths (Basic) 2023 · Paper 430/2/1 · Question 38

Surface Areas and Volumes 4 marks Hard

A wooden toy is shown in the picture. This is a cuboidal wooden block of dimensions

14

\times

17

\times

4

cm. On its top there are seven cylindrical hollows for bees to fit in. Each cylindrical hollow is of height

3

cm and radius

2

cm.

(i)Find the volume of wood carved out to make one cylindrical hollow.[1]
(ii)Find the lateral surface area of the cuboid to paint it with green colour.[1]
(iii)(a)Find the volume of wood in the remaining cuboid after carving out seven cylindrical hollows.[2]
(iii)(b)OR Find the surface area of the top surface of the cuboid to be painted yellow.[2]

Answer

(i)

\frac{264}{7} \approx 37.71

^{3}

; (ii)

248

^{2}

; (iii a)

688

^{3}

; (iii b)

150

^{2}

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