Surface area and Volume (Part - 3)

1. A cubical box has each edge 9 cm and another cuboidal box is 10 cm long , 10 cm wide and 8 cm high .

a). Which box has the greater lateral surface area and by how much ?

b). Which box has the smaller total surface area and by how much ?

Sol. a). Side of cubical box l = 9 cm

Curved surface area of cubical box = 4 l^2 cm^2 = 4 ( 9 )^2 cm^2 = 4 * 81 cm^2 = 324 cm^2

Length of cuboidal box l = 9 cm^2 breadth = 10 cm^2 and height = 8 cm^2

Curved surface area of cuboidal box = 2 ( l + b ) h cm^2 = 2 * ( 9 + 10 ) * 8 cm^2

Curved surface area of cuboidal box = 2 * 19 * 8 cm^2 = 304 cm^2

Difference between surface area of two boxes = 324 cm^2 – 304 cm^2 = 20 cm^2

Hence , the curved surface area of cubical box is more than cuboidal box by 20 cm^2 .

b). Side of cubical box l = 9 cm

Total surface area of cubical box = 6 l^2 cm^2 = 6 ( 9 )^2 cm^2 = 6 * 81 cm^2 = 486 cm^2

Length of cuboidal box l = 9 cm^2 breadth = 10 cm^2 and height = 8 cm^2

Total surface area of cuboidal box = 2 ( l b + b h + h l ) cm^2 = 2 * ( 9 * 10 + 10 * 8 + 8 * 9 ) cm^2

Total surface area of cuboidal box = 2 ( 90 + 80 + 72 ) cm^2

Total surface area of cuboidal box = 2 ( 242 ) cm^2 = 484 cm^2

Difference between total surface area of two boxes = 486 cm^2 – 484 cm^2 = 2 cm^2

Hence , the curved surface area of cubical box is more than cuboidal box by 2 cm^2 .

2. A small indoor green house is made of entirely of glass panes held together with tape . It is 28 cm long , 25 cm wide and 25 cm high .

a). What is the area of glass ?

b). How much tape is needed for all the 12 edges ?

sol. a). Length of green house l = 28 , breath b = 25 cm and height = 25 cm

Total surface area of green house = 2 ( l b + b h + h l ) cm^2 = 2 * ( 28 * 25 + 25 * 25 + 25 * 28 ) cm^2

Total surface area of green house = 2 * ( 700 + 625 + 700 ) cm^2 = 2 * 2025 cm^2

Total surface area of green house = 4050 cm^2

Hence , the area of glass for greenhouse is 4050 cm^2

b). Length of green house l = 28 cm , breath = 25 cm and height h = 25 cm

Length of tape for all 12 edges = 4 ( l + b + h ) cm = 4 ( 28 + 25 + 25 ) cm

Length of tape for all 12 edges = 4 * 78 cm = 312 cm

Hence , for all 12 edges , 312 cm tape is required .

3. A cubical box has each edge 9 cm and another cuboidal box is 8 cm long , 10 cm wide and 8 cm high .

a). Which box has the greater lateral surface area and by how much ?

b). Which box has the smaller total surface area and by how much ?

Sol. a). Side of cubical box l = 9 cm

Curved surface area of cubical box = 4 l^2 cm^2 = 4 ( 9 )^2 cm^2 = 4 * 81 cm^2 = 324 cm^2

Length of cuboidal box l = 8 cm^2 breadth = 10 cm^2 and height = 8 cm^2

Curved surface area of cuboidal box = 2 ( l + b ) h cm^2 = 2 * ( 8 + 10 ) * 8 cm^2

Curved surface area of cuboidal box = 2 * 18 * 8 cm^2 = 288 cm^2

Difference between surface area of two boxes = 324 cm^2 – 288 cm^2 = 36 cm^2

Hence , the curved surface area of cubical box is more than cuboidal box by 36 cm^2 .

b). Side of cubical box l = 9 cm

Total surface area of cubical box = 6 l^2 cm^2 = 6 ( 9 )^2 cm^2 = 6 * 81 cm^2 = 486 cm^2

Length of cuboidal box l = 8 cm^2 breadth = 10 cm^2 and height = 8 cm^2

Total surface area of cuboidal box = 2 ( l b + b h + h l ) cm^2 = 2 * ( 8 * 10 + 10 * 8 + 8 * 8 ) cm^2

Total surface area of cuboidal box = 2 ( 80 + 80 + 64 ) cm^2

Total surface area of cuboidal box = 2 ( 224 ) cm^2 = 448 cm^2

Difference between total surface area of two boxes = 486 cm^2 – 448 cm^2 = 38 cm^2

Hence , the curved surface area of cubical box is more than cuboidal box by 38 cm^2 .

maths ncert solutions

4. A small indoor green house is made of entirely of glass panes held together with tape . It is 25 cm long , 20 cm wide and 20 cm high .

a). What is the area of glass ?

b). How much tape is needed for all the 12 edges ?

sol. a). Length of green house l = 25 , breath b = 20 cm and height = 20 cm

Total surface area of green house = 2 ( l b + b h + h l ) cm^2 = 2 * ( 25 * 20 + 20 * 20 + 20 * 25 ) cm^2

Total surface area of green house = 2 * ( 500 + 400 + 500 ) cm^2 = 2 * 1400 cm^2

Total surface area of green house = 2800 cm^2

Hence , the area of glass for greenhouse is 2800 cm^2

b). Length of green house l = 25 cm , breath = 20 cm and height h = 20 cm

Length of tape for all 12 edges = 4 ( l + b + h ) cm = 4 ( 25 + 20 + 20 ) cm

Length of tape for all 12 edges = 4 * 65 cm = 260 cm

Hence , for all 12 edges , 260 cm tape is required .

Milan Tomic

Hi. I’m Designer of Blog Magic. I’m CEO/Founder of ThemeXpose. I’m Creative Art Director, Web Designer, UI/UX Designer, Interaction Designer, Industrial Designer, Web Developer, Business Enthusiast, StartUp Enthusiast, Speaker, Writer and Photographer. Inspired to make things looks better.