Question

internal and external diameters of a hollow hemisphere are 8cm and 10cm respectively what its TSA​

Answer 1

$\huge\underline\mathbb\red{GIVEN:-}$

• Internal diameter of hollow hemisphere = 8 cm
• External diameter of hollow hemisphere = 10 cm

$\huge\underline\mathbb\red{TO\:FIND:-}$

Find the T.S.A. of hemisphere = ?

$\huge\underline\mathbb\red{SOLUTION:-}$

We have given that the internal diameter of hemisphere = 8 cm

$\rm{Internal\: Radius =\frac{Internal \:diameter}{2}= \frac{8}{2}}$

$\large\rm\blue{Internal\:Radius= 4\: cm}$

The external diamtere of hemisphere = 10 cm

$\rm{External\: radius =\frac{External\:Diameter}{2}=\frac {10}{2}}$

$\large\rm\blue{External \:Radius= 5\: cm}$

Let the internal radius of hemisphere be (r)

and,

external radius of hemisphere be (R)

∴ To find the T.S.A. of hemisphere, we use the formula:-$\bf{ 2π{r}^{2} + 2π{R}^{2} + π({R}^{2} -{ r}^{2}) }$

$\implies$$\bf{2π({r}^{2} + {R}^{2}) + π({R}^{2} - {r}^{2})}$

$\implies$$\bf{2π[{(4)}^{2}+ {(5)}^{2}] + π[{(5)}^{2} - {(4)}^{2}]}$

$\implies$$\bf{2π(16+25) +π(25-16)}$

$\implies$ $\bf{2π(41) +π(9)}$

$\implies$ $\bf{2 \times\frac {22}{7} \times41 + \frac{22}{7} \times 9}$

$\implies$ $\bf{\frac{22}{7}\times(2 \times 41 + 9)}$

$\implies$ $\bf{\frac{22}{7} \times(82 + 9)}$

$\implies$ $\bf{\frac{22}{7}\times91}$

$\implies$ $\bf{ 22 \times13}$

$\implies$ $\bf{286 \:{cm}^{2}}$

$\large\underline\mathbb\red{FINAL\:ANSWER:-}$

$\huge{\boxed{\boxed{\bf{\blue{T.S.A. = 286\:{cm}^{2}}}}}}$

Thus, the T.S.A. of hemisphere is 286 cm²

Answer 2

Answer:

$\implies$ The T.S.A of hemisphere is 286cm².

$\large\underline\mathrm{Given:-}$

• Internal diameter of hollow hemisphere = 8cm
• External diameter of a hollow hemisphere = 10cm

$\large\underline\mathrm{To \: find}$

• The T.S.A of hemisphere = ?

$\large\underline\mathrm{Solution}$

$\implies$ Internal Radius = (Internal Diameter)/2 = 8/2

$\implies$ Internal Radius = 4cm

$\implies$ External Radius = External Diameter = 10/2

$\implies$ External Radius = 5

• Let the internal radius of hemisphere be (r) and external radius of hemisphere be (R).

$\implies$ 2πr² + 2πr² + π(R² - r²)

$\implies$ 2π(r² + R²) + π(R² - r²)

$\implies$ 2π(4² + 5²) + π(5² - 4²)

$\implies$ 2π(16 + 15) + π(25 - 16)

$\implies$ 2π(41) + π(9)

$\implies$ 2 × 22/7 × 41 + 22/7 × 9

$\implies$ 22/7 × (82 + 9)

$\implies$ 22/7 × 91

$\implies$ 22 × 13

$\implies$ 286cm²

Thus,

The T.S.A of hemisphere is 286cm².