Page 1 Surface and volume of cube, cuboid, and cylinder Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m 2 .The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting= 13 Rs/m 2 , l=10m , b=5m , h=6m To find cost of painting four walls we first need to find the surface area of four walls . Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h Vertical surface area of cuboid=180 m 2 . Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting =180×13 =2340 Therefore Cost of Painting the four wall is 2340 Rs Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m 3 .what will be the weight of the pillar. Given: For Pillar [cuboid] Length =600cm= 600 100 =6m Breadth =55cm= 55 100 =0.55m Height=25cm= 25 100 =0.25m =2(10+5)×6 =2(15)×6 =180 l h b Tip: Remember to convert dimensions from cm to m as weight per cube is given in m 3 Page 2 Surface and volume of cube, cuboid, and cylinder Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m 2 .The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting= 13 Rs/m 2 , l=10m , b=5m , h=6m To find cost of painting four walls we first need to find the surface area of four walls . Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h Vertical surface area of cuboid=180 m 2 . Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting =180×13 =2340 Therefore Cost of Painting the four wall is 2340 Rs Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m 3 .what will be the weight of the pillar. Given: For Pillar [cuboid] Length =600cm= 600 100 =6m Breadth =55cm= 55 100 =0.55m Height=25cm= 25 100 =0.25m =2(10+5)×6 =2(15)×6 =180 l h b Tip: Remember to convert dimensions from cm to m as weight per cube is given in m 3 Solution Volume of Beam pillar[cuboid]= ?? × ?? × h =6×0.55×0.25 =0.825 m 3 Weight of pillar=Volume of pillar×weight of volume per m 3 =0.825×200 =165 Kg Weight of pillar=165 Kg Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a playground. Find the area of playground in m 2 . Solution: The Diameter cylindrical roller =40 cm Radius of cylindrical roller(r) = 40 2 = 20 cm Length of cylindrical roller (h) =140 cm Curved surface area of cylindrical roller = 2 ???? h =2 × 2 2 7 × 20 × 140 =17600 cm 2 =17600/10000 =1.76 m 2 Area covered in one revolution is = curved surface area of cylinder = 1.76 m 2 Total Area of Playground= No. of revolutions × curved surface area of cylinder = 350×1.76 =616 m 2 Area of Playground= 616 m 2 . Tip: Since the shape of roller is like cylinder, we will use formula for cylinder. Note: Since we are converting cm 2 to m 2 we need to divide it by 100×100 Page 3 Surface and volume of cube, cuboid, and cylinder Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m 2 .The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting= 13 Rs/m 2 , l=10m , b=5m , h=6m To find cost of painting four walls we first need to find the surface area of four walls . Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h Vertical surface area of cuboid=180 m 2 . Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting =180×13 =2340 Therefore Cost of Painting the four wall is 2340 Rs Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m 3 .what will be the weight of the pillar. Given: For Pillar [cuboid] Length =600cm= 600 100 =6m Breadth =55cm= 55 100 =0.55m Height=25cm= 25 100 =0.25m =2(10+5)×6 =2(15)×6 =180 l h b Tip: Remember to convert dimensions from cm to m as weight per cube is given in m 3 Solution Volume of Beam pillar[cuboid]= ?? × ?? × h =6×0.55×0.25 =0.825 m 3 Weight of pillar=Volume of pillar×weight of volume per m 3 =0.825×200 =165 Kg Weight of pillar=165 Kg Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a playground. Find the area of playground in m 2 . Solution: The Diameter cylindrical roller =40 cm Radius of cylindrical roller(r) = 40 2 = 20 cm Length of cylindrical roller (h) =140 cm Curved surface area of cylindrical roller = 2 ???? h =2 × 2 2 7 × 20 × 140 =17600 cm 2 =17600/10000 =1.76 m 2 Area covered in one revolution is = curved surface area of cylinder = 1.76 m 2 Total Area of Playground= No. of revolutions × curved surface area of cylinder = 350×1.76 =616 m 2 Area of Playground= 616 m 2 . Tip: Since the shape of roller is like cylinder, we will use formula for cylinder. Note: Since we are converting cm 2 to m 2 we need to divide it by 100×100 Q.4) The curved surface area of cylinder is 154 cm 2 . The total surface area of the cylinder is thrice the curved surface area. Find the volume of cylinder.[ p=22/7] Given: curved surface area of cylinder (2 ???? h )= 154 cm 2 Solution Curved surface area of cylinder ( ???? ?? ?? )= 154 cm 2 ?? × ???? ?? × ?? × ?? = ?????? h= ?????? ?? × ???? h= ?? . ?? cm Volume of Cylinder= ?? ?? ?? ?? = ???? ?? × ?? × ?? × ?? . ?? = 539 cm 3 Volume of Cylinder= 539 cm 3 : Total surface area of cylinder= 2 ×curved surface area 2 ???? h + 2 ?? ?? 2 = 3 × 154 154 +2 pr 2 = 462 2 pr 2 =462– 154 2 pr 2 =308 2 × 2 2 7 × ?? 2 = 308 r 2 = 3 0 8 × 7 2× 2 2 r 2 =49 r=7 Page 4 Surface and volume of cube, cuboid, and cylinder Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m 2 .The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting= 13 Rs/m 2 , l=10m , b=5m , h=6m To find cost of painting four walls we first need to find the surface area of four walls . Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h Vertical surface area of cuboid=180 m 2 . Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting =180×13 =2340 Therefore Cost of Painting the four wall is 2340 Rs Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m 3 .what will be the weight of the pillar. Given: For Pillar [cuboid] Length =600cm= 600 100 =6m Breadth =55cm= 55 100 =0.55m Height=25cm= 25 100 =0.25m =2(10+5)×6 =2(15)×6 =180 l h b Tip: Remember to convert dimensions from cm to m as weight per cube is given in m 3 Solution Volume of Beam pillar[cuboid]= ?? × ?? × h =6×0.55×0.25 =0.825 m 3 Weight of pillar=Volume of pillar×weight of volume per m 3 =0.825×200 =165 Kg Weight of pillar=165 Kg Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a playground. Find the area of playground in m 2 . Solution: The Diameter cylindrical roller =40 cm Radius of cylindrical roller(r) = 40 2 = 20 cm Length of cylindrical roller (h) =140 cm Curved surface area of cylindrical roller = 2 ???? h =2 × 2 2 7 × 20 × 140 =17600 cm 2 =17600/10000 =1.76 m 2 Area covered in one revolution is = curved surface area of cylinder = 1.76 m 2 Total Area of Playground= No. of revolutions × curved surface area of cylinder = 350×1.76 =616 m 2 Area of Playground= 616 m 2 . Tip: Since the shape of roller is like cylinder, we will use formula for cylinder. Note: Since we are converting cm 2 to m 2 we need to divide it by 100×100 Q.4) The curved surface area of cylinder is 154 cm 2 . The total surface area of the cylinder is thrice the curved surface area. Find the volume of cylinder.[ p=22/7] Given: curved surface area of cylinder (2 ???? h )= 154 cm 2 Solution Curved surface area of cylinder ( ???? ?? ?? )= 154 cm 2 ?? × ???? ?? × ?? × ?? = ?????? h= ?????? ?? × ???? h= ?? . ?? cm Volume of Cylinder= ?? ?? ?? ?? = ???? ?? × ?? × ?? × ?? . ?? = 539 cm 3 Volume of Cylinder= 539 cm 3 : Total surface area of cylinder= 2 ×curved surface area 2 ???? h + 2 ?? ?? 2 = 3 × 154 154 +2 pr 2 = 462 2 pr 2 =462– 154 2 pr 2 =308 2 × 2 2 7 × ?? 2 = 308 r 2 = 3 0 8 × 7 2× 2 2 r 2 =49 r=7 Surface area and volume of Cone and Frustrum Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area and volume? Given: Radius of cone(r) = 3 cm Height of cone(h) = 4 cm Solution: First we will find slant height of cone (l) = v h 2 + ?? 2 l = v4 2 + 3 2 l = v16 + 9 l = v25 l = 5 cm Total Surface Area of Cone = ???? ( ?? + ?? ) = 2 2 7 × 3 × (3 + 5) = 2 2 7 × 3 × 8 = 75.428 cm 2 Volume of cone = 1 3 ?? ?? 2 h = 1 3 × 2 2 7 × 3 2 × 4 = 22×3×4 7 =37.714 cm 3 Page 5 Surface and volume of cube, cuboid, and cylinder Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m 2 .The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting= 13 Rs/m 2 , l=10m , b=5m , h=6m To find cost of painting four walls we first need to find the surface area of four walls . Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h Vertical surface area of cuboid=180 m 2 . Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting =180×13 =2340 Therefore Cost of Painting the four wall is 2340 Rs Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m 3 .what will be the weight of the pillar. Given: For Pillar [cuboid] Length =600cm= 600 100 =6m Breadth =55cm= 55 100 =0.55m Height=25cm= 25 100 =0.25m =2(10+5)×6 =2(15)×6 =180 l h b Tip: Remember to convert dimensions from cm to m as weight per cube is given in m 3 Solution Volume of Beam pillar[cuboid]= ?? × ?? × h =6×0.55×0.25 =0.825 m 3 Weight of pillar=Volume of pillar×weight of volume per m 3 =0.825×200 =165 Kg Weight of pillar=165 Kg Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a playground. Find the area of playground in m 2 . Solution: The Diameter cylindrical roller =40 cm Radius of cylindrical roller(r) = 40 2 = 20 cm Length of cylindrical roller (h) =140 cm Curved surface area of cylindrical roller = 2 ???? h =2 × 2 2 7 × 20 × 140 =17600 cm 2 =17600/10000 =1.76 m 2 Area covered in one revolution is = curved surface area of cylinder = 1.76 m 2 Total Area of Playground= No. of revolutions × curved surface area of cylinder = 350×1.76 =616 m 2 Area of Playground= 616 m 2 . Tip: Since the shape of roller is like cylinder, we will use formula for cylinder. Note: Since we are converting cm 2 to m 2 we need to divide it by 100×100 Q.4) The curved surface area of cylinder is 154 cm 2 . The total surface area of the cylinder is thrice the curved surface area. Find the volume of cylinder.[ p=22/7] Given: curved surface area of cylinder (2 ???? h )= 154 cm 2 Solution Curved surface area of cylinder ( ???? ?? ?? )= 154 cm 2 ?? × ???? ?? × ?? × ?? = ?????? h= ?????? ?? × ???? h= ?? . ?? cm Volume of Cylinder= ?? ?? ?? ?? = ???? ?? × ?? × ?? × ?? . ?? = 539 cm 3 Volume of Cylinder= 539 cm 3 : Total surface area of cylinder= 2 ×curved surface area 2 ???? h + 2 ?? ?? 2 = 3 × 154 154 +2 pr 2 = 462 2 pr 2 =462– 154 2 pr 2 =308 2 × 2 2 7 × ?? 2 = 308 r 2 = 3 0 8 × 7 2× 2 2 r 2 =49 r=7 Surface area and volume of Cone and Frustrum Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area and volume? Given: Radius of cone(r) = 3 cm Height of cone(h) = 4 cm Solution: First we will find slant height of cone (l) = v h 2 + ?? 2 l = v4 2 + 3 2 l = v16 + 9 l = v25 l = 5 cm Total Surface Area of Cone = ???? ( ?? + ?? ) = 2 2 7 × 3 × (3 + 5) = 2 2 7 × 3 × 8 = 75.428 cm 2 Volume of cone = 1 3 ?? ?? 2 h = 1 3 × 2 2 7 × 3 2 × 4 = 22×3×4 7 =37.714 cm 3 Q.2) The volume of the cone is 352 cm 3 and its height is 21 cm what will be the radius of cone? Given: volume of cone (v)= 352 cm 3 Height of cone = 21 cm Solution Volume of cone (v) = 1 3 ?? ?? 2 h 352= 1 3 × 2 2 7 × ?? 2 × 21 3 5 2 2 2 = ?? 2 16 = ?? 2 ? ?? = 4 ( ?? ?? ???? ???? ?????? ?? ???? ?????? h ???? ???? ) Ans: The radius of cone is 4 cm. Q.3)The height of frustum is 4 cm and it’s radii are 6 cm and 3 cm. Find curved surface area and volume of frustum. Given: Height of frustum (h) = 4 cm Base Radius (r 1 ) = 6 cm Upper Radius (r 2 ) =3 cm Solution: Slant Height of the Frustum (l) = ? h 2 + ( ?? 1 - ?? 2) 2 l = ?4 2 + (6 - 3) 2 l = v16 + 9 l = v25 l =5 cm Curved surface area of frustum = ?? ( ?? 1 + ?? 2 ) ??Read More

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