Q. 14

The outer and inner diameter of a hollow hemi–spherical vessel are 43 cm and 42 cm. Find the cost of colouring the vessel at 7 paise per square cm.

Answer :


The hemispherical bowl will look like as shown


To find the cost required to paint we first need to calculate its total surface area


Total surface area will include the area of outter curved surface the inner curved surface and the flat surface as shown


Diameter of outer surface = 43 cm


Radius of outer surface = ro = cm = 21.5 cm


Diameter of inner surface = 42 cm


Radius of inner surface = ri = cm = 21 cm


Curved surface area of hemisphere = 2πr2


outter curved surface area = 2πro2


= 2 × π ×


= π cm2


= 924.5π cm2


inner curved surface area = 2πri2


= 2 × π × 212


= 882π cm2


The flat area can be found by subtracting the inner circle area from outter circle area


flat area = πro2 – πri2


= π(21.5)2 – π(21)2


= 462.25π – 441π


= 21.25π cm2


Total surface area of hemispherical vessel = outter curved surface area + inner curved surface area + flat area


Total surface area of hemispherical vessel = 924.5π + 882π + 21.25π = 1827.75π cm2


Now cost of colouring 1 cm2 is 7 paise


So, cost of colouring 1827.75π cm2 = 7 × 1827.75 × π


= 7 × 1827.75 ×


= 1827.75 × 22


= 40210.5 paise


100 paise is 1 Rs


40210.5 paise = = 402.105 Rs


Therefore, cost of colouring the vessel is 402.105 Rs


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Surface Area and Volume49 mins
Surface Area and Volumes43 mins
Quiz | Surface Area and Volumes42 mins
Champ Quiz | Area Related with the Circle45 mins
Quiz | Area Related with Circles47 mins
Short Cut Trick to Find Area of Triangle43 mins
Idioms and Phrases43 mins
Goprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and Nomenclature52 mins
Agriculture and its Importance35 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses