a solid in the shape of fustrum of a cone the diameter of the two circular ends are 60 cm and 36 cm and the height is 9 cm find the area of its whole surface area and the volume
Answers
The volume of frustum of Cone is 5292π cm³ & Total Surface area of frustum of Cone = 1944π cm².
Step-by-step explanation:
SOLUTION :
GIVEN :
Diameter of lower end of frustum of cone = 60 cm
Radius of the lower end of the frustum of cone( R) = 60/2 = 30 cm
Diameter of upper end of frustum of cone , r = 36 cm
Radius of the upper end of the frustum of cone( r) = 36/2 = 18 cm
Height of the frustum of Cone = 9 cm
Slant height of bucket ( l)= √(h² + (R- r)²
l =√9² + (30 - 18)² = √81 + 12²
l =√81+ 144
l = √225 = 15 cm
l = 15 cm
Volume frustum of Cone = π/3 (R² + r² + Rr) h
= ⅓ × π (30² + 18² + 30× 18)× 9
= ⅓ π (900 + 324 + 540)× 9
= ⅓ π × 1764 × 9
= π × 1764 × 3
= 5292π cm³
Volume of frustum of Cone = 5292π cm³
Total Surface area of frustum of Cone = π(R + r)l + πR² + πr²
= π(30 + 18) × 15 + π(30)² + π(18)²
= π(48×15 + 900 + 324)
= π(720 + 1224)
= 1944π cm²
Total Surface area of frustum of Cone = 1944π cm²
Hence, the volume of frustum of Cone is 5292π cm³ & Total Surface area of frustum of Cone = 1944π cm².
Please mark as brainliest
please follow me