Question

A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. ($\mathrm{\pi }=3.14$)

Answer 1

Given:
Diameter of the test tube = 20 mm
Height of the test tube = 15 cm
∴ Radius of the test tube = $\frac{20}{2}$ mm = 10 mm = 1 cm
Now,
Height of the cylindrical portion = Height of the test tube $-$ Radius of the hemispherical portion
= 15 cm $-$ 1 cm
= 14 cm
Volume of the cylindrical portion = $\mathrm{\pi }$r²h
= 3.14 × (1)² × 14
= 43.96 cm³
Volume of the hemispherical portion = $\frac{2}{3}\mathrm{\pi }{r}^3$
= $\frac{2}{3}\times 3.14\times (1{)}^3$
= 2.09 cm³

Thus, we have:
Volume of the test tube = Volume of the cylindrical portion + Volume of the hemispherical portion
= 43.96 cm³ + 2.09 cm³
= 46.05 cm³