Question

The total surface area of solid hemisphere is 462 cm? If the curved surface area of it is 308 cm2, then the area of the base of the hemisphere is
(A) 308 cm2
(B) 231 cm2
(C) 154 cm cm2
(D) 2 1078 cm​

Answer 1

Answer:

The total surface area of solid hemisphere is 462 cm? If the curved surface area of it is 308 cm2, then the area of the base of the hemisphere is

(A) 308 cm2

(B) 231 cm2

(C) 154 cm cm2

(D) 2 1078 cm

Step-by-step explanation:

b Is the answer.

Answer 2

Answer:

154 $cm^{2}$.

Step-by-step explanation:

Given:- Total surface area of solid Hemisphere is 462 $cm^{2}$.

              Curved surface area = 308 $cm^{2}$.

To Find:- area of the base of the Hemisphere.

Solution:-

As we know,

Total surface area of a hemisphere = $3\pi r^{2}$, where r = radius of the solid hemisphere.

Curved surface area of a hemisphere = $2\pi r^{2}$.

Area of base of a hemisphere = $\pi r^{2}$.

We can either use total surface area or curved surface area to find the radius of the hemisphere.

$3\pi r^{2}$ = 462

⇒ $r^{2}$ = 462/3π

⇒ $r^{2}$ = 154/π

⇒ $r^{2}$ = 154 × 7/22

⇒ $r^{2}$ = 49

⇒ r = +7, -7.

Since radius of a hemisphere cannot be negative.

∴ r = 7cm.

Now, base area of the hemisphere = $\pi r^{2}$

                                                          = 22/7 × 7 × 7

                                                          = 22 × 7

                                                          = 154 $cm^{2}$.

Therefore, the base area of the hemisphere = 154 $cm^{2}$.

The correct option is C) 154 $cm^{2}$.

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