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A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is $3.5 cm$ and the total wood used in the making of toy is $166.83 cm 3$ . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ₹ 10 per $cm 2$ . $Use π = 227$

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9.5 cm and Rs.725

8.25 cm and Rs.725

8.25 cm and Rs.770

9.5 cm and Rs.770

answer is D.

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Detailed Solution

It is given that, the total volume, and radius of the hemisphere is

V = 166.83 cm 3

and

r = 3.5 cm

.
The volume of a cone is expressed as,

V = 13 π r 2 h

, where

r

and h be the radius and height of a cylinder.
The volume of hemisphere is expressed as,

V = 23 π r 3

, where

r

is the radius.
Suppose the height of the cone is

h

.
Thus, the total volume of cone and the hemisphere is,

V = 13 π r 2 h + 23 π r 3 ⇒ 166.83 = π 3.5 2 h + 2 3.5 ⇒ h = 13 − 7 ⇒ h = 6 cm

So, the height of toy is,

H = h + r ⇒ H = 6 + 3.5 ⇒ H = 9.5 cm

The cost of painting the hemi-spherical part of the toy at the rate of rupees

10

per

cm 2

is,

Thus, the height of the toy and the cost of painting the hemi-spherical part of the toy is 9.5 cm and Rs.770 respectively.
Therefore, option (4) is correct.

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