Height of conical part = Height of cylindrical part (h) = 2.4 cm Diameter of cylindrical part = 1.4 m, so, the radius of cylindrical part (r) = 0.7 m Slant height of cylindrical part (l) = √(r²+ h²) = √((0.7)² + (2.4)²) = √(0.49 + 5.76) = √(6.25) = 2.5 The total surface area of the remaining solid =Read more
Height of conical part = Height of cylindrical part (h) = 2.4 cm
Diameter of cylindrical part = 1.4 m, so, the radius of cylindrical part (r) = 0.7 m
Slant height of cylindrical part (l) = √(r²+ h²)
= √((0.7)² + (2.4)²) = √(0.49 + 5.76) = √(6.25) = 2.5
The total surface area of the remaining solid
= CSA of cylindrical + CSA of conical part + Area of base of cylinder
= 2πrh + πrl + πr²
= 2 × 22/7 × 0.7 × 2.4 + 22/7 × 0.7 × 2.5 + 22/7 × 0.7 × 0.7
= 4.4 × 2.4 + 2.2 × 2.5 × 0.7 = 10.56 + 5.50 + 1.56 = 17.60 cm².
The maximum diameter of hemishere = Side of cubical block (a) = 7 cm Radius of hemisphere = a/2 = 3.5 cm The surface are of the soild = Surface area of cubical block + CSA of hemisphere - Area of base of hemisphere = 6a² + 2πr² - πr² = 6a² + πr² = 6 × 7² + 22/7 × 3.5² = 294 + 38.5 = 332.5 cm² Hence,Read more
The maximum diameter of hemishere = Side of cubical block (a) = 7 cm
Radius of hemisphere = a/2 = 3.5 cm
The surface are of the soild
= Surface area of cubical block + CSA of hemisphere – Area of base of hemisphere
= 6a² + 2πr² – πr²
= 6a² + πr²
= 6 × 7² + 22/7 × 3.5² = 294 + 38.5 = 332.5 cm²
Hence, the surface area of the solid is 332.5 cm²
The maximum daimeter of hemisphere = side of cubical block = l Radius of hemisphere (r) = l/2 The surface area of the remaining solid = TSA of cubical block + CSA of hemisphere - Area of base of hemisphere = 6l² + 2πr² - πr² = 6l² + πr² = 6l² + π(l/2)² = (6 + π/4)l² Hence, the surface area of the reRead more
The maximum daimeter of hemisphere = side of cubical block = l
Radius of hemisphere (r) = l/2
The surface area of the remaining solid
= TSA of cubical block + CSA of hemisphere – Area of base of hemisphere
= 6l² + 2πr² – πr²
= 6l² + πr²
= 6l² + π(l/2)²
= (6 + π/4)l²
Hence, the surface area of the remaining solid is (6 + π/4)l².
Radius of cone = 3.5 cm Height of cone = 15.5 - 3.5 = 12 cm Radius of hemisphere = 3.5 cm Slant height of cone (l) = √r² +h² = √((3.5)² + (12)²) = √(12.25 + 144) = √(156.25) = 12.5 The total surface area of the toy = CSA of cone + CSA of hemisphere = πrl + 2πr² = 22/7 × 3.5 × 12.5 + 2 × 22/7 ×3.5² =Read more
Radius of cone = 3.5 cm
Height of cone = 15.5 – 3.5 = 12 cm
Radius of hemisphere = 3.5 cm
Slant height of cone (l)
= √r² +h² = √((3.5)² + (12)²) = √(12.25 + 144) = √(156.25) = 12.5
The total surface area of the toy
= CSA of cone + CSA of hemisphere
= πrl + 2πr²
= 22/7 × 3.5 × 12.5 + 2 × 22/7 ×3.5²
= 137.5 + 77
= 214.5 cm²
Hence, the total surface area of the toy is 572 cm²
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Height of conical part = Height of cylindrical part (h) = 2.4 cm Diameter of cylindrical part = 1.4 m, so, the radius of cylindrical part (r) = 0.7 m Slant height of cylindrical part (l) = √(r²+ h²) = √((0.7)² + (2.4)²) = √(0.49 + 5.76) = √(6.25) = 2.5 The total surface area of the remaining solid =Read more
Height of conical part = Height of cylindrical part (h) = 2.4 cm
See lessDiameter of cylindrical part = 1.4 m, so, the radius of cylindrical part (r) = 0.7 m
Slant height of cylindrical part (l) = √(r²+ h²)
= √((0.7)² + (2.4)²) = √(0.49 + 5.76) = √(6.25) = 2.5
The total surface area of the remaining solid
= CSA of cylindrical + CSA of conical part + Area of base of cylinder
= 2πrh + πrl + πr²
= 2 × 22/7 × 0.7 × 2.4 + 22/7 × 0.7 × 2.5 + 22/7 × 0.7 × 0.7
= 4.4 × 2.4 + 2.2 × 2.5 × 0.7 = 10.56 + 5.50 + 1.56 = 17.60 cm².
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
The maximum diameter of hemishere = Side of cubical block (a) = 7 cm Radius of hemisphere = a/2 = 3.5 cm The surface are of the soild = Surface area of cubical block + CSA of hemisphere - Area of base of hemisphere = 6a² + 2πr² - πr² = 6a² + πr² = 6 × 7² + 22/7 × 3.5² = 294 + 38.5 = 332.5 cm² Hence,Read more
The maximum diameter of hemishere = Side of cubical block (a) = 7 cm
See lessRadius of hemisphere = a/2 = 3.5 cm
The surface are of the soild
= Surface area of cubical block + CSA of hemisphere – Area of base of hemisphere
= 6a² + 2πr² – πr²
= 6a² + πr²
= 6 × 7² + 22/7 × 3.5² = 294 + 38.5 = 332.5 cm²
Hence, the surface area of the solid is 332.5 cm²
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
The maximum daimeter of hemisphere = side of cubical block = l Radius of hemisphere (r) = l/2 The surface area of the remaining solid = TSA of cubical block + CSA of hemisphere - Area of base of hemisphere = 6l² + 2πr² - πr² = 6l² + πr² = 6l² + π(l/2)² = (6 + π/4)l² Hence, the surface area of the reRead more
The maximum daimeter of hemisphere = side of cubical block = l
See lessRadius of hemisphere (r) = l/2
The surface area of the remaining solid
= TSA of cubical block + CSA of hemisphere – Area of base of hemisphere
= 6l² + 2πr² – πr²
= 6l² + πr²
= 6l² + π(l/2)²
= (6 + π/4)l²
Hence, the surface area of the remaining solid is (6 + π/4)l².
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Radius of cone = 3.5 cm Height of cone = 15.5 - 3.5 = 12 cm Radius of hemisphere = 3.5 cm Slant height of cone (l) = √r² +h² = √((3.5)² + (12)²) = √(12.25 + 144) = √(156.25) = 12.5 The total surface area of the toy = CSA of cone + CSA of hemisphere = πrl + 2πr² = 22/7 × 3.5 × 12.5 + 2 × 22/7 ×3.5² =Read more
Radius of cone = 3.5 cm
See lessHeight of cone = 15.5 – 3.5 = 12 cm
Radius of hemisphere = 3.5 cm
Slant height of cone (l)
= √r² +h² = √((3.5)² + (12)²) = √(12.25 + 144) = √(156.25) = 12.5
The total surface area of the toy
= CSA of cone + CSA of hemisphere
= πrl + 2πr²
= 22/7 × 3.5 × 12.5 + 2 × 22/7 ×3.5²
= 137.5 + 77
= 214.5 cm²
Hence, the total surface area of the toy is 572 cm²