Jawaban:

√5/4.

Penjelasan dengan langkah-langkah:

a. The volume of a cone is given by Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height. The volume of a sphere is given by Vsphere = (4/3)πr^3, where r is the radius of the sphere.

Plugging in the values, we get:

Vcone = (1/3)π(5)^2(10) = 250/3π

Vsphere = (4/3)π(5)^3 = 500/3π

The ratio of the volumes is Vcone/Vsphere = (250/3π)/(500/3π) = 1/2.

b. The curved surface area of a cone is given by Lcone = πrℓ, where r is the radius of the base and ℓ is the slant height of the cone. The curved surface area of a sphere is given by Lsphere = 4πr^2, where r is the radius of the sphere.

To find the slant height of the cone, we use the Pythagorean theorem:

h^2 + r^2 = ℓ^2

10^2 + 5^2 = ℓ^2

ℓ = √125

Plugging in the values, we get:

Lcone = π(5)(√125) = 25π√5

Lsphere = 4π(5)^2 = 100π

The ratio of the curved surface areas is Lcone/Lsphere = (25π√5)/(100π) = √5/4.