Question

A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. the diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. find the total surface area of the vessel.

Answer 1

Answer:

1134 square m.

Step-by-step explanation:

Diameter of hemispherical bowl is 14 cm

Radius = diameter/ 2 = 7 cm

Height of the vessel is 13 cm

Height of cylinder = Height of vessel - radius of hemisphere = 13-7 = 6cm

Total area of vessel : $2(\text{CSA of cylinder}+{\text{CSA of Hemisphere})$

= $2(2\pi rh +2\pi r^2)$

= $2\times 2 \pi \times r(h +r)$

= $2\times 2\times \frac{22}{7}\times7(7+6)$

= $1134$

Thus the area of the vessel is 1134 square m.

Answer 2

Answer:

the diameter of the hemispherical bowl = 14 cm

the radius of the hemisphere r = 14/2 = 7cm

the curved surface area of the bowl =2πr²

                                                            =2×22/7×7×7

                                                           =308cm²

the total height of the vessel = 13 cm

the height of the cylindrical part = 13-7= 6 cm

the surface area of the cylinder =2πrh

                                                    =2×22/7×7×6

                                                    =264cm²

total surface area of the vessel = surface area of the cylinder + surface area of the sphere

                                                     =308+264

                                                     =572cm²