Answer:
Volume = 502 cm^3
Surface area = 501 cm^2
- to the nearest whole number.
Explanation:
The radius of the base of the cylinder = 1/2 * 7 = 3.5 cm.
Volume of a cylinder = π r^2 h.
The volume of the cylinder without the holes = 22/7 * (3.5)^2 * 15 cm^3.
The diameter of a cone = 2/5 * 15 = 6 cm so its radius = 3 cm.
So the volume of a cone = 1/3 * 22/7 * 3^2 * 4 cm^3
Therefore the volume of the solid with the 2 conical holes
= 22/7 * (3.5)^2 * 15 - 2 * 1/3 * 22/7 * 3^2 * 4
= 577.5 - 75.429
= 502.07 cm^3
Surface area of the cylinder without the holes
= 2π r^2 + 2π rh
= 2 * 22/7 * 3.5^2 + 2 * 22/7 * 3.5 * 15
Diameter of the cone = 2/5 * 15 = 6 cm so its radius = 3.
Surface are aof a cone = πr(s + r) where s = slant height of the cone.
s = √(r^2 + h^2) = √(3^2 + 4^2)
= 5
So surface area of a cone = 22/7 * 3(5+3) = 75.429 cm^2
Surface area of the base of a cone = 22/7 * 3^2
Surface area of the whole solid with the the 2 holes
= 2 * 22/7 * 3.5^2 + 2 * 22/7 * 3.5 * 15 + 2 * 75.429 - 2 * 22/7 * 3^2
(Note we have to subtract 2 * surface areas of base of cone. Only the curved part of the cones contribute to total surface area).)
2 * 22/7 * 3.5^2 + 2 * 22/7 * 3.5 * 15 + 2 * 75.429 - 2 * 22/7 * 3^2
= 407 + 150.86 - 56.57
= 501.29 cm^2.