Question

Find the curved surface area and total surface area of a hollow hemisphere whose outer and inner radii are $4.3$ cm and $2.1$ cm respectively.

• A. $36.98\pi {\text{cm}}^2$, $59.26\pi {\text{cm}}^2$
• B. $48.1\pi {\text{cm}}^2$, $58.22\pi {\text{cm}}^2$
• C. $36.98\pi {\text{cm}}^2$, $59.88\pi {\text{cm}}^2$
• D. $49.1\pi {\text{cm}}^2$, $5.32\pi {\text{cm}}^2$

Answer 1

The correct option is C $36.98\pi {\text{cm}}^2$, $59.88\pi {\text{cm}}^2$

We have,

$R=4.3cm$

$r=2.1cm$

We know that the curved surface area of the hollow hemisphere

$=2\pi R^2$

So,

$=2\pi (4.3{)}^2$

$=36.98\pi c{m}^2$

We know that the total surface area of the hollow hemisphere

$=2\pi R^2+2\pi r^2+\pi (R^2-r^2)$

So,

$=2\pi (4.3{)}^2+2\pi (2.1{)}^2+\pi \left(\right(4.3{)}^2-\left(2.1{)}^2\right)$

$=36.98\pi +8.82\pi +\pi \left(\right(4.3{)}^2-\left(2.1{)}^2\right)$

$=36.98\pi +8.82\pi +14.08\pi$

$=59.88\pi c{m}^2$

Hence, this is the answer.