Question

Atoy is in the form of a cone mounted on a hemisphere of the same diameter. The diameter
of the base and the height of the cone are 6 cm and 4 cm respectively. Determine the
surface area of the toy. [use pi = 3.14]​

Answer 1

$\red{\underline{\huge{</p><h2>✪<strong><u>ᴀɴsᴡᴇʀ</u></strong>✪</h2><p>}}}$

• Surface Area of the toy is $103.62\:cm^2.$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• A toy in the form of a cone mounted on a hemisphere of the same diameter.

• D = 6 cm, H = 4 cm.

☆ᴛᴏ ғɪɴᴅ☆

• Surface Area of toy.

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

Slant height of the cone is given by

$\to l = \sqrt{H^2 + R^2}$

$\to l = \sqrt{4^2 + 3^2}$

$\to l = \sqrt{16 + 9}$

$\to l = \sqrt{25}$

$\to l = 5$

Surface Area of the cone(without base) is given by

$\to S_{cone} = \pi Rl$

$\to S_{cone} = \pi \times 3\times 5$

$\to S_{cone} = 15\pi$

Surface Area of the hemesphere is given by

$\to S_{hem} = \frac{1}{2}[4\pi R^2]$

$\to S_{hem} = 2\pi R^2$

$\to S_{hem} = 2\pi 3^2$

$\to S_{hem} = 18\pi$

Total Surface Area of toy is given by

$\to S = S_{cone} + S_{hem}$

$\to S = 15\pi + 18\pi$

$\to S = 33\pi$

$\to S ≈ 33\times 3.14$

$\to S ≈ 103.62\:cm^2$

Answer 2

Answer:

A toy in the form of a cone mounted on a hemisphere of the same diameter.

D = 6 cm, H = 4 cm.

☆ᴛᴏ ғɪɴᴅ☆

Surface Area of toy.

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

Slant height of the cone is given by

\to l = \sqrt{H^2 + R^2}→l=

H

2

+R

2

\to l = \sqrt{4^2 + 3^2}→l=

4

2

+3

2

\to l = \sqrt{16 + 9}→l=

16+9

\to l = \sqrt{25}→l=

25

\to l = 5→l=5

Surface Area of the cone(without base) is given by

\to S_{cone} = \pi Rl→S

cone

=πRl

\to S_{cone} = \pi \times 3\times 5→S

cone

=π×3×5

\to S_{cone} = 15\pi→S

cone

=15π

Surface Area of the hemesphere is given by

\to S_{hem} = \frac{1}{2}[4\pi R^2]→S

hem

=

2

1

[4πR

2

]

\to S_{hem} = 2\pi R^2→S

hem

=2πR

2

\to S_{hem} = 2\pi 3^2→S

hem

=2π3

2

\to S_{hem} = 18\pi→S

hem

=18π