Review and Practice

A solid is a cylinder (radius $4$, height $10$) with a hemisphere (radius $4$) on top. Find the total volume. Use π ≈ $3.14$.

• 1Cylinder volume: $3.14\times 16\times 10=502.4$
• 2Full sphere volume would be: $\frac{4}{3}\times 3.14\times 64$ ≈ $267.95$. Halve it for the hemisphere: ≈ $133.97$
• 3Add: $502.4+133.97$

Answer: ≈ $636.37$

Find the total exposed surface area of the same solid.

• 1Cylinder's curved surface: $2\times 3.14\times 4\times 10=251.2$
• 2Cylinder's bottom circle: $3.14\times 16=50.24$
• 3Hemisphere's curved surface: $2\times 3.14\times 16=100.48$
• 4The cylinder's top circle is covered by the hemisphere — excluded
• 5Add: $251.2+50.24+100.48$

Answer: ≈ $401.92$