Question

A cone has radius 5x cm and a height 12x cm.A sphere has radius r cm.The cone has the same total surface area as the sphere.Show that r²=45÷2 x². (The curved surface area,A, of a cone with radius r and slant height l is A=πrl.) (The surface area,A, of a sphere with radius r is A=4πr².)

someone please help with this last one

Answer 1

r^2 = 45÷2 x^2

Explanation:

Details of cone:

Radius(r) = 5x cm

Height(h) = 12x cm

Slant height(l) = √(12x^2 + 5x^2)

l = 13x cm

Total surface area of a cone (T. S. A) = πrl + πr²

T. S. A = π * 5x * 13x + π5x^2

T.S.A = π65x^2 + π5x^2

T.S.A = π65x^2 + π25x^2

T.S.A = 90πx^2 - - - - - (1)

Details of sphere:

Radius (r) = r cm

Total surface area = 4πr²

Total Surface area of sphere= 4πr²cm - - - (2)

Equating (1) and (2) to calculate r

4πr² = 90πx^2

r^2 = 90πx^2 / 4π

r^2 = 90π (x^2) / 4π

r^2 = 45/2 (x^2) ;

r^2 = 45÷2 x^2

Hence the proof