A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
Answers
Answer:
Total surface area of the solid is 418 cm² and Volume of solid is 641.67 cm³
Step-by-step explanation:
SOLUTION :
Given :
Total height of solid= 19 cm
Diameter of Cylinder and hemisphere = 7 cm
Radius of Cylinder = radius of hemisphere= 7/2= 3.5 cm
Height of hemisphere = radius of hemisphere = 7/2 cm
Height of 2 hemisphere = 2× 7/2= 7 cm
Height of Cylinder= Total height of solid - Height of 2 hemisphere
Height of Cylinder(h) = 19 - 7 = 12 cm
Volume of solid,V = Volume of Cylinder Volume of two hemispheres
V = πr²h + 2 × 2/3πr³
V = πr²h + 4/3πr³
V = πr²(h + 4/3 r)
V = 22/7 × 7/2 × 7/2 (12 + 4/3 × 7/2)
V = 77/2 (12 + 14/3)
V = 77/2 [(36+14)/3]
V = 77/2 [50/3)
V = (77 × 25)/3
V = 1925/3 = 641.67
V = 641.67 cm³
Volume of solid = 641.67 cm³
Total surface area of the solid = surface area of cylinder + surface area of two hemispheres
= 2πrh + 2(2πr²)
= 2πrh + 4πr²
= 2πr(h+2r)
= 2×(22/7)×7/2 (12 + 2 × 7/2)
= 22 (12 + 7)
= 22 × 19
= 418 cm²
Total surface area of the solid = 418 cm²
Hence, Total surface area of the solid is 418 cm² and Volume of solid is 641.67 cm³.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
TSA OF SOLID =418 cm2
VOLUME OF SOLID =641.67