a small cone of radius 5cm and slant height 13 cm is mounted on a bigger solid cone of radius 8 cm and slant height 17cm with common base. find the surface area and volume of the combined figures.

Asked by divyanshusingh10thb16 | 5th Mar, 2022, 10:39: PM

Expert Answer:

Curved surface area of a cone = pi r l
Total space surface space area space equals space CSA space of space small space cone space plus thin space CSA space of space bigger space cone space plus space open parentheses πr subscript 2 squared space minus space πr subscript 1 squared close parentheses
equals πr subscript 1 straight l subscript 1 space plus space πr subscript 2 straight l subscript 2 space plus space open parentheses πr subscript 2 squared space minus space πr subscript 1 squared close parentheses
equals space straight pi open parentheses 5 cross times 13 space plus thin space 8 cross times 17 space plus space open parentheses 289 space minus space 169 close parentheses close parentheses
equals straight pi open parentheses 65 plus 136 plus 120 close parentheses
equals straight pi open parentheses 321 close parentheses
equals 321 straight pi space cm squared
Total space volume equals 1 third πr subscript 1 squared straight h subscript 1 space plus space 1 third πr subscript 2 squared straight h subscript 2
straight h subscript 1 equals square root of straight i subscript 1 squared minus straight r subscript 1 squared end root equals square root of 144 equals 12 space cm
straight h subscript 2 equals square root of straight i subscript 2 squared minus straight r subscript 2 squared end root equals square root of 225 equals 15 space cm

Total space volume space equals space 1 third straight pi open parentheses 300 plus 960 close parentheses equals 1 third straight pi cross times 1260 equals 420 straight pi space cm cubed

Answered by Renu Varma | 9th Mar, 2022, 10:33: AM