UPSKILL MATH PLUS

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### Theory:

1. The diameter of an orange is $$8 \ cm$$. Calculate the total surface area of the half orange.

Solution:

Diameter of an orange, $$d$$ $$=$$ $$8 \ cm$$

Radius of an orange, $$r$$ $$=$$ $\frac{d}{2}=\frac{8}{2}=4\phantom{\rule{0.147em}{0ex}}\mathit{cm}$

A half orange is in the shape of a hemisphere.

Total surface area of a hemisphere $$=$$ $$3 \pi r^2$$ sq. units

$$=$$ $3×\frac{22}{7}×{4}^{2}$

$$=$$ $3×\frac{22}{7}×16$

$$=$$ $$150.86$$

The total surface area of the half orange is $$150.86 \ cm^2$$.

2. If the inner and outer radius of the hemispherical shell is $$3 \ cm$$ and $$5 \ cm$$, find the thickness and the curved surface area of the shell.

Solution:

Inner radius, $$r$$ $$=$$ $$3 \ cm$$

Outer radius, $$R$$ $$=$$ $$5 \ cm$$

Thickness $$=$$ $$R - r$$

$$=$$ $$5 - 3 = 2$$

The thickness of the shell is $$2 \ cm$$.

Curved surface area $$=$$ $$2 \pi (R^2 + r^2)$$ sq. units

$$=$$ $2×\frac{22}{7}×\left({5}^{2}+{3}^{2}\right)$

$$=$$ $2×\frac{22}{7}×\left(25+9\right)$

$$=$$ $2×\frac{22}{7}×34$

$$=$$ $$213.7$$

The curved surface area of the hemispherical shell is $$213.7$$ $$cm^2$$.

Important!
The value of $$\pi$$ should be taken as $$\frac{22}{7}$$ unless its value is shared in the problem.