Q2 of 32 Page 260

A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7 cm. and its volume is of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal

Given that, The radius of the base(r) of the cone is 7 cm and its volume is of the hemisphere.

∵ circular base of cone is joined with the plane surface of the hemisphere,


⇒ radius of hemisphere = radius of base of cone = 7 cm


Also,vol. of cone = vol. of hemisphere



⇒ h = 3r


⇒h = 3 × 7


⇒h = 21 cm


Also, slant height(l) = √ r2 + h2


⇒ l = √ 72 + 212


⇒ l = √ 490


⇒ l = 22.13


⇒ Slant Height of cone (l) = 22.13 cm


Now, surface area of toy = surface area of cone + surface area of hemisphere


⇒ surface area of toy = πrl + 2πr2


= πr(l + 2r)




= 794.86 cm2


More from this chapter

All 32 →
8

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 10 cm. and its radius of the base is of 3.5 cm, find the total surface area of the article.

 1

An iron pillar consists of a cylindrical portion of 2.8 m. height and 20 cm. in diameter and a cone of 42 cm. height surmounting it. Find the weight of the pillar if 1cm3 of iron weighs 7.5 g.

 3

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 7 cm.

 4

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub