Question

The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.

Answer 1

A = 1443.65 sq. cm (Maybe)

Though you do not have a figure shown. 

Answer 2

This is an incomplete question, here is the complete question.

The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.

(1) 1727 cm²

(2) 2355 cm²

(3) 2041 cm²

(4) 6699 cm²

Answer : The surface area of the figure is, 1727 cm²

Step-by-step explanation :

The formula for curved surface area of triangle is:

$A=\pi \times r\times l$

where,

r and l are radius and slant height of triangle.

The formula for curved surface area of cylinder is:

$A=2\pi \times r\times h$

where,

r and h are radius and height of cylinder.

The formula for area of circle is:

$A=\pi r^2$

where,

r is radius circle.

Now we have to calculate the surface area of total figure.

Surface area of total figure = Surface area of triangle + Surface area of cylinder + Area of circle

Surface area of total figure = $\pi \times r\times l+2\pi \times r\times h+\pi r^2$

Surface area of total figure = $\pi \times r(l+2h+r)$

Given:

r = 10 cm

h = 16 cm

l = 13 cm

Now put all the given values in this formula, we get:

Surface area of total figure = $3.14\times 10\times (13+2\times 16+10)$

Surface area of total figure = 1727 cm²

Thus, the surface area of the figure is, 1727 cm²