Question

As a part of school project, Mishika and Sahaj created a bird-bath from the cylindrical log of wood by scooping out the hemispherical depression from one end of the cylinder as shown in the figure given. Cylinder has a length 2 m out of which 0.6 m is in earth and the diameter is 1.4 m.

On the basis of the above information, answer the following questions:

(i) Write the radius of the hemispherical depression.   [1]

(ii) Find the volume of water that can be filled in the hemispherical depression in terms of π.   [1]

(iii) (a) Find the total surface area of log of wood above the ground after making the bird-bath.   [2]

OR

(iii) (b) Compute the volume of log of wood above the ground after making the bird-bath.   [2]

Answer 1

(i) Radius = `1.4/2`

= 0.7 m

(ii) Volume of hemisphere = `2/3 πr^3`

= `2/3 π xx 0.7 xx 0.7 xx 0.7`

= `2/3 π xx 7/10 xx 7/10 xx 7/10`

= `686/3000 π`

= `343/1500 π`

= 0.2286 πm³ (approx)

(iii) (a) Total surface area of log of wood above the ground

= 2πrh + 2πr²

= 2πr(h + r)

= `2 xx 22/7 xx 0.7 xx (1.4 + 0.7)`

= `44/10 xx 2.1`

= 9.24 m²

OR

(iii) (b) Volume of required part

= `πr^2h - 2/3 πr^3`

= `πr^2 (h - 2/3 r)`

= `22/7 xx 0.7 xx 0.7 xx (1.4 - 2/3 xx 0.7)`

= `22/7 xx 0.49 xx (1.4 - 0.467)`

= 1.436 m³ (approx)