Question

a sokid sphere in the form of a cone surmonded on a hemisphere of the same radius .If the height of the cone is 24 cm and radius of the hemisphere is 7.Find the volume and surface area of the solid​

Answer 1

Answer:

Volume = 1950.67 cub. cm

Surface area = 858 sq. cm

Explanation:

Given a solid such that it consists of a cone surmounted on a hemisphere.

Radius of cone = Radius of hemisphere = 7 cm

Height if the cone, h = 24 cm

Therefore, we will get,

=> Slant height, l = √{(24)^2 + (7)^2}

=> l = √(576+49)

=> l = √625

=> l = 25

Therefore, we have,

Slant height, l = 25 cm

Now, To find the Volume of solid,

=> v = vol.(cone+hemisphere)

$= > v = \frac{2}{3}\pi {r}^{3} + \frac{1}{3} \pi {r}^{2} h \\ \\ = > v = \frac{r}{3} \pi(2 {r}^{2} + hr) \\ \\ = > v = \frac{1}{3} \times \frac{22}{7} \times 7(2 \times 49 + 24 \times 7) \\ \\ = > v = \frac{22}{3} (98 + 168) \\ \\ = > v = \frac{22}{3} \times 266 \\ \\ = > v = 1950.67 \: \: {cm}^{3}$

Therefore, we will get,

Volume of solid = 1950.67 cubic cm.

Now, to find the Surface area of solid,

=> a = L.S.A ( cone+hemisphere)

=> a = πrl+2πr^2

=> a = πr(l+2r)

=> a = 22/7 × 7 (25 + 14)

=> a = 22 × 39

=> a = 858

Therefore, we get,

Surface area of solid = 858 sq. cm