Question

A newspaper is rolled into a cylindrical shape of approximate diameter 4cm It is wrapped for posting with a strip of paper which goes about 2 1/2 times round the newspaper Use the value 3 for π to find the approximate length of the wrapping paper. And 2. Calculate the total surface area of a solid cone of slant hight 10cm and base diameter 10 cm.Use the value 3.14 for π

Answer 1

30 cm

`863.5\ \text{cm}^2`

Explanation:

d = Diameter of cylinder = 4 cm

n = Number of times the strip of paper is turned =
`2(1)/(2)=2.5`

Diameter of the cylinder will be approximately equal to the diameter of the paper wound. Length of one turn will be circumference of the paper

Circumference of the paper

`c=\pi d\\\Rightarrow c=3* 4\\\Rightarrow c=12\ \text{cm}`

Total length of the paper will be the number of turns multiplied by the length of one turn

`l=nc\\\Rightarrow l=2.5* 12\\\Rightarrow l=30\ \text{cm}`

Length of the strip of paper is 30 cm.

2.

l = Slant height = 10 cm

d = Base diameter = 10 cm

r = Radius of base =
`r=(d)/(2)=(10)/(2)=5\ \text{cm}`

Total surface area of cone is given by

`S=\pi r^2+\pi rl\\\Rightarrow S=\pi r(r+rl)\\\Rightarrow S=3.14* 5(5+5*10)\\\Rightarrow S=863.5\ \text{cm}^2`

The total surface area of cone is
`863.5\ \text{cm}^2`.