Question

99. A small hemisphere of radius 4 cm is mounted on a larger hemisphere of radius
7 cm with common base. Find the surface area and volume of the combined
figure. (Take n = 3.14)​

Answer 1

Step-by-step explanation:

Surface area = 33 cm2

Volume = 279cm3

Answer 2

Answer:

combined surface area =  511.82 cm²

combined volume = 851.97 cm³

Step-by-step explanation:

given, radius of small hemisphere = 4 cm

radius of large hemisphere = 7 cm

total surface area of hemisphere = 3πr²

TSA of large hemisphere = 3 × 3.14 × 7² = 461.58 cm²

Curved surface area of hemisphere = 2πr²

CSA of small hemisphere = 2 × 3.14 ×  4² = 100.48 cm²

base area of small hemisphere = πr² = 3.14 × 4² = 50.24 cm²

surface area of the combined figure = TSA of large hemisphere +CSA of small hemisphere - base area of small hemisphere

combined surface area = 461.58 + 100.48 - 50.24 = 511.82 cm²

combined surface area = 511.82 cm²

volume of hemisphere = $\frac{2}{3}$πr³

volume of small hemisphere = $\frac{2}{3}$ × 3.14 × 4³ =  133.97 cm³

volume of large hemisphere = $\frac{2}{3}$ × 3.14 × 7³ = 718 cm³

combined volume = volume of small hemisphere +volume of large hemisphere = 133.97 + 718 = 851.97 cm³

combined volume = 851.97 cm³