# Mensuration-15

### From Homeworkwiki

**A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area.**

**Solution:** Radius of the hemisphere = 7 cm

Total height of the toy = 31 cm

Therefore, height of the conical part = 31 - 7 = 24 cm

Slant height of the conical part, l = √(r^{2} + h^{2})

= √(7^{2} + 24^{2})

= √(49 + 576) = √625 = 25 cm

Surface area of the conical part = π r l = 22/7 x 7 x 25 = 550 cm^{2}

Surface area of the hemispherical part = 2 π r^{2} = 2 x 22/7 x 7 x 7

= 308 cm^{2}

Total surface area of the toy = surface area of the conical part + Surface area of the hemispherical part

= 550 + 308 = 858 cm^{2}