The interior of building is in the form of a cylinder of diameter 4m and height 3 5m ,surmounted by - Maths - Surface Areas and Volumes

Question

The interior of building is in the form of a cylinder of
diameter 4m and height 3 5m ,surmounted by a cone of the same base
with vertical angle as a right angle Find the surface area (curved)
and volume of the interior of the building

Ayush Jha · Accepted Answer

The radius of cone and cylinder(r) = 2 m

Height of cylinder(h) = 3.5 m

Height of cone = Radius of cone = 2 m (As the vertical angle is right angle)

So the slant height of the cone is

$l = \sqrt{2^{2} + 2^{2}} = 2 \sqrt{2} m$

So the curved surface area of the building

$= 2 π r h + π r l = π r (2 h + l) = \frac{22}{7} (2) (7 + 4) = \frac{484}{7} m^{2}$

Volume of the building is

$= π r^{2} h + \frac{1}{3} π r^{2} H = π r^{2} (h + \frac{H}{3}) = \frac{22}{7} (4) (3.5 + \frac{2}{3}) = \frac{1100}{21} m^{3}$

The interior of building is in the form of a cylinder of diameter 4m and height 3.5m ,surmounted by a cone of the same base with vertical angle as a right angle. Find the surface area (curved) and volume of the interior of the building.