Question

Find the surface area and round to the nearest tenth

Answer 1

area cylinder= pi× r² × h, but the drawing shows only half of the cylinder so: area= (pi×r²×h)/2

area= (pi×(6/2)²×25)/2 (the radius is 6/2 because the

drawing indicates the whole

diameter)

area= 225pi / 2

area≈353.43cm³

Answer 2

413.9 cm²

Explanation:

The total surface area of the solid is the sum of the curved area, semicircular end area, and rectangular base area.

Half a cylinder

The area of the curved surface is the lateral area of half a cylinder. The area of the semicircular ends is half the end area of a cylinder. The area of these surfaces together is half the area of a cylinder:

A = 1/2(2πr)(r +h) = πr(r +h)

The radius is half the given diameter, so the area of the half-cylinder we can see is ...

A = π(3 cm)(3 cm +25 cm) = 84π cm²

Rectangular base

The rectangular bottom of the figure is hidden from view. Its dimensions are given as 6 cm wide by 25 cm long. Its area is given by the formula for the area of a rectangle:

A = LW

A = (25 cm)(6 cm) = 150 cm²

Total area

The total surface area of the figure is the sum of the half-cylinder area and the area of the base:

total area = (84π +150) cm² ≈ 413.9 cm²

The surface area of the figure is about 413.9 square centimeters.