Question

1. The diagram represents a cone.

The height of the cone is 12 cm.
The diameter of the base of the cone is 10 cm.
Calculate the curved surface area of the cone.

2. A sphere has a volume of 500 m​3​.
(b) Calculate the radius of the sphere. Give your answer correct to 3
significant figures.

Answer 1

1. The curved surface area of the cone is 282.74 cm²

2. Radius of sphere r = 4.924 m

Explanation:

1. Height of cone = 12 cm

Diameter of base of cone = 10 cm

Surface Area of cone = ?

The formula used is:
`A=\pi r(r+√(h^2+r^2))\\`

h= 12 cm

r = diameter/2 r = 10/2 = 5 cm

Putting values and finding surface area

`A=\pi r(r+√(h^2+r^2))\\A=3.14*5 (5+√((12)^2+(5)^2))\\A=15.7 (5+√(144+25))\\A=15.7 (5+√(169))\\A=15.7 (5+13)\\A=15.7(18)\\A=282.74 \ cm^2`

So, the curved surface area of the cone is 282.74 cm²

2. Sphere of Volume = 500 m³

We need to find radius of sphere

The formula used is:
`Volume=(4)/(3)\pi r^3`

Putting values and finding radius of sphere

`Volume=(4)/(3)\pi r^3\\500=(4)/(3)*3.14* r^3\\500=4.186*r^3\\=> r^3=(500)/(4.186)\\r^3=119.446\\Taking \ cube \ root \ on \ both \ sides.\\\sqrt[3]{r^3}=\sqrt[3]{119.446}\\r= 4.924 \ m\\`

So, Radius of sphere r = 4.924 m