A, B, C and D are points on the circumference of a circle, centre O.
ADE and BCE are straight lines
.
Work out the size of angle CED.
Give a reason for each stage of your working.
Show your working. Label each angle you find (eg.
ODC) and give a reason on the same line.
98
98
31°
72°
48°
B



Answer :

Answer:

The total surface area of the solid \(T\), formed by joining a cone and hemisphere with a 7 cm diameter each, can be calculated by summing the surface areas of both shapes.

To find the total surface area

(

total

)

(A

total

) of the solid

T , formed by joining a solid cone and a solid hemisphere, we need to calculate the surface areas of the cone and hemisphere separately and then add them together.

Given:

- Diameter of the base of the cone = 7 cm

- Diameter of the hemisphere = 7 cm

First, let's draw a diagram to represent the solid \(T\):

```

__________

/ \

/ \

/ \

/___________________\

```

Now, let's calculate the surface area of each component:

1. Surface area of the cone (\(A_{\text{cone}}\)):

- The formula for the surface area of a cone is

cone

=

cone

(

cone

+

cone

)

A

cone

=πr

cone

(r

cone

+l

cone

) , where

cone

r

cone

is the radius of the base and

cone

l

cone

is the slant height.

- Since the diameter of the cone's base is 7 cm, the radius

(

cone

)

7

/

2

=

3.5

(r

cone

)is7/2=3.5 cm.

- We need to find the slant height

(

cone

)

(l

cone

) . Using the Pythagorean theorem,

cone

=

cone

2

+

cone

2

l

cone

=

r

cone

2

+h

cone

2

, where \(h_{\text{cone}}\) is the height of the cone.

- As the cone's height is not given, let's assume it's the same as the radius, \(h_{\text{cone}} = r_{\text{cone}} = 3.5\) cm.

- Substituting the values into the formula, we get

cone

=

×

3.5

×

(

3.5

+

3.

5

2

+

3.

5

2

)

.

A

cone

=π×3.5×(3.5+

3.5

2

+3.5

2

).

2. Surface area of the hemisphere

(

hemisphere

)

(A

hemisphere

) :

- The formula for the surface area of a hemisphere is

hemisphere

=

2

hemisphere

2

.

7

,

(

hemisphere

)

7

/

2

=

3.5

.

A

hemisphere

=2πr

hemisphere

2

.−Sincethediameterofthehemisphereis7cm,theradius(r

hemisphere

)is7/2=3.5cm.

- Substituting the value into the formula, we get

hemisphere

=

2

×

3.

5

2

.

A

hemisphere

=2π×3.5

2

.

Finally, the total surface area

(

total

)

(A

total

) of the solid

T is the sum of the surface areas of the cone and hemisphere:

total

=

cone

+

hemisphere

A

total

=A

cone

+A

hemisphere

Substitute the calculated values to find the total surface area.

The question probably maybe: What is the total surface area of the solid \( T \), formed by joining a solid cone with a diameter of 7 cm at its base to a solid hemisphere with a diameter of 7 cm?