Question

For a cricket tournament involving 8 countries, a special trophy, as shown below, is designed. The height and diameter of the cylindrical part are 14 cm and 6 cm respectively and the diameter of the spherical ball on the top is 7 cm.

Based on the above information, answer the following questions:

(i) Find the total height of the trophy excluding the wooden part.   [1]

(ii) Find the difference between the radius of sphere and that of cylinder.   [1]

(iii) (a) If the cylindrical part and spherical part are separated and gold plated overall, find the total surface area to be gold plated.   [2]

OR

(iii) (b) Find the volume of the metal used in making the trophy, assuming that the metal is completely filled in it.   [2]

Answer 1

Given:

Cylindrical part:

Height (h) = 14 cm

Diameter = 6 cm

Radius (r_​c) = `6/2` = 3 cm

Spherical part:

Diameter = 7 cm

Radius (r_s) = `7/2` = 3.5 cm

(i) Total height of the trophy excluding wooden part:

Total height = Height of cylinder + Diameter of sphere

= 14 + 7

= 21 cm

(ii) Difference between radius of sphere and cylinder:

= r_s – r_c

= 3.5 – 3

= 0.5 cm

(iii) (a) Total surface area to be gold plated:

Total Area = Total surface area of cylinder + Surface area of sphere

= `2πr_c(h + r_c) + 4πr_s^2`

= `2 xx 22/7 xx 3(14 + 3) + 4 xx 22/7 xx 3.5 xx 3.5`

= `132/7 xx 17 + 4 xx 22/7 xx 7/2 xx 7/2`

= `2244/7 + 154`

= 320.57 + 154

= 474.57 cm²

OR

(iii) (b) Volume of metal used:

Total Volume = Volume of cylinder + Volume of sphere

= `πr_c^2h + 4/3 πr_s^3`

= `22/7 xx 3 xx 3 xx 14 + 4/3 xx 22/7 xx 3.5 xx 3.5 xx 3.5`

= `22 xx 9 xx 2 + 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2`

= `396 + (11 xx 49)/3`

= `396 + 539/3`

= 396 + 179.67

= 575.67 cm³