Composite Solids

A solid is made of a cylinder (radius $3$, height $5$) with a cone (same radius $3$, height $4$) on top. Find the total volume. Use π ≈ $3.14$.

• 1Cylinder volume: $3.14\times 9\times 5=141.3$
• 2Cone volume: $\frac{1}{3}\times 3.14\times 9\times 4=113.04÷3=37.68$
• 3Add: $141.3+37.68$

Answer: $178.98$

Using the same solid, find the total EXPOSED surface area.

• 1Cylinder's curved surface (still exposed): $2\times 3.14\times 3\times 5=94.2$
• 2Cylinder's bottom circle (still exposed): $3.14\times 9=28.26$
• 3Cone's slant height: √($3^2+4^2$) = $5$. Cone's curved surface (still exposed): $3.14\times 3\times 5=47.1$
• 4The cylinder's TOP circle and the cone's BASE are joined together — hidden inside the solid, and excluded
• 5Add the exposed parts: $94.2+28.26+47.1$

Answer: $169.56$