A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere.

0 votes
1 view
asked Mar 27 in Class X Maths by muskan15 (-2,429 points)

A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere. The radius of the base of the cone is 3.5 meters and its volume is two thirds of the hemisphere. Calculate the height of the cone and the surface area of buoy correct to two places of decimal.

Please log in or register to answer this question.

1 Answer

0 votes
answered Mar 27 by navnit40 (-3,230 points)

According to question

2/3(Volume of hemisphere) = Volume of cone

2/3(2/3πr3) = 1/3πr2h

4/9(3.5)3 = 1/3(3.5)2.h

h = 4 × 3.5 × 3.5 × 3.5 × 3/3.5 × 3.5 × 9

= 42.0/9 = 14/3 m = 4.67 m

Now surfaces area of buoy = Surface area of right cone + surface area of hemisphere

= πrl + 2πr2

= πr(l + 2r)

= 22/7 × 3.5(35/6 + 2 × 3.5)

= 11 × (5.83 + 7)

= 11 × 12.83

= 141.13 sq. m.

Related questions

0 votes
1 answer
...