Chapter 10.6, Problem 31E

To determine

To calculate the lateral surface area of cone.

Answer to Problem 31E

259 m²

Explanation of Solution

Given Information: Cylinder Height h = 5 m, Cone Diameter d = 7 m., Slant Height l = 6.5 m. and $\pi =\frac{22}{7}$

Formula Used:

Surface area of solid = Lateral Surface area of Cone + Surface area of Cylinder

Lateral Surface area of Cone = $\pi rl$ , Surface area of Cylinder = $2\pi r(h+r)$ , Radius = $\frac{Diameter}{2}$

Calculation:

Lateral Surface area of Cone Diameter d = 7 m., Slant Height l = 6.5 m. and $\pi =\frac{22}{7}$

First find Radius r.

Hence,

Radius = $\frac{Diameter}{2}$

Put the value of diameter to find radius of Cone

So, Radius = $\frac{7}{2}$ m

Lateral Surface area of Cone = $\pi rl$

Radius r = $\frac{7}{2}$ m., Slant Height l = 6.5 m. and $\pi =\frac{22}{7}$

Now put the value of r, s and $\pi$ to find Lateral Surface area of Cone

Lateral Surface area of Cone = $\frac{22}{7}\times \frac{7}{2}\times 6.5$ m²

Hence,

Lateral Surface area of Cone = $71.5$ m²

Surface Area of Cylinder- Diameter d = 7 m., Height h = 5 m. and $\pi =\frac{22}{7}$

First find Radius r.

Hence,

Radius = $\frac{Diameter}{2}$

Put the value of diameter to find radius of Cone

So, Radius = $\frac{7}{2}$ m

Surface area of Cylinder = $2\pi r(h+r)$

Radius r = $\frac{7}{2}$ m., Height h = 5 m. and $\pi =\frac{22}{7}$

Now put the value of r, h and $\pi$ to find Surface area of Cylinder

Surface area of Cylinder = $2\times \frac{22}{7}\times \frac{7}{2}\times \left(5+\frac{7}{2}\right)$ m²

So,

Surface area of Cylinder = $22\times \frac{17}{2}$ m²

Hence,

Surface area of Cylinder = 187 m²

Surface Area of Solid-

Surface Area of Solid = Lateral Surface area of Cone + Surface area of Cylinder

Now put value of Lateral Surface area of Cone and Surface area of Cylinder

Surface Area of Solid = $71.5$ m²+ 187 m²

Surface Area of Solid = 258.5 m²

Nearest Surface Area of Solid = 259 m²