A cubical block of side 14 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
3 points
1330 sqcm
332.5 sqcm
1445.5 sqcm
Answers
Answer:
The diameter of the hemisphere is 14cm
The surface area of the solid is 1484cm²
Step-by-step explanation:
The largest diameter of the hemisphere will be 14 because it covered the whole top of the cube .
We then proceed to finding the surface area of the solid
Since it has not been specified whether the hemisphere was closed or open we treat it like a closed hemisphere.
The formula for finding the surface area of the closed hemisphere is
2πr²
Since the diameter is 14 cm the radius is half of that which is 7 cm
2 × 22/7 × 7 × 7 = 308 cm²
We then find the surface area of the cube
The cube has six faces hence
We find the area of one face then we multiply by six which is the total number of faces
14 × 14 = 196 cm²
196 × 6 = 1176 cm²
We then add both the areas to find the total surface area of the solid.
1176 + 308 = 1484 cm²
Given:
A cubical block of side 14 cm is surmounted by a hemisphere.
To find:
What is the greatest diameter the hemisphere can have?
Find the surface area of the solid.
Solution:
From given, we have,
The side of a cubical block = a = 14 cm
⇒ The diameter of the hemisphere surmounted = d = 14 cm
Therefore, the greatest diameter the hemisphere can have is equal to the side of a cubical block.
⇒ The radius = r = d/2 = 14/2 = 7 cm
∴ r = 7 cm
Surface area of the solid = Area of cube + Curved surface area of hemisphere - Base area of hemisphere
⇒ Surface area of the solid = 6a² + 2πr² - πr²
⇒ Surface area of the solid = 6a² + πr²
= 6(14)² + 22/7 × 7²
= 1176 + 22 × 7
= 1176 + 154
= 1330
∴ The surface area of the solid is 1330 sq cm.