Question

The total surface area of a solid hemisphere is 75 times the area of circle whose diameter is 6 cm what is the radius of the hemisphere ?

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Total surface area of solid hemisphere=75}{\times}\textsf{Area of circle having radius 6cm}$

$\underline{\textsf{To find:}}$

$\textsf{Radius of the hemisphere}$

$\underline{\textsf{Solution:}}$

$\textsf{Let r be the radius of the hemisphere}$

$\textsf{Total surface area of solid hemisphere=75}{\times}\textsf{Area of circle having radius 3cm}$

$\implies\mathsf{3\,\pi\,r^2=75{\times}\pi\,(3)^2}$

$\implies\mathsf{r^2=25{\times}9}$

$\implies\mathsf{r=5{\times}3}$

$\implies\textsf{r=15 cm}$

$\underline{\textsf{Answer:}}$

$\textsf{Radius of the hemisphere is 15 cm}$

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Answer 2

Given :-

• The total surface area of a solid hemisphere is 75 times the area of circle whose diameter is 6 cm .

To Find :-

• what is the radius of the hemisphere ?

Solution :-

we know that,

• Total surface area of hemisphere is = 3 * π * (radius)².
• Area of circle = π * (diameter/2)² .

Let us assume that radius of hemisphere is R cm.

given that,

→ Total surface area of hemisphere = 75 * Area of circle .

Putting all values we get :-

→ 3 * π * R² = 75 * π * (6/2)²

π will be cancel from both sides,

→ 3 * R² = 75 * 3 * 3

dividing by 3 both sides,

→ R² = 75 * 3

→ R² = 25 * 3 * 3

→ R² = 5² * 3²

→ R² = (5 * 3)²

→ R² = (15)²

square root both sides now,

→ R = 15 cm. (Ans.)

Hence, radius of hemisphere is 15 cm.

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