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The volume of the composite figure is the third option 385.17 cubic centimeters.
Step-by-step explanation:
Step 1:
The composite figure consists of a cone and a half-sphere on top.
We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.
The radius is 4 cm and the height is 15 cm.
The volume of the cone :
cubic cm.
Step 3:
The area of a half-sphere is half of a full sphere.
The volume of a sphere is given by multiplying with π and the cube of the radius (r³).
Here the radius is 4 cm. We take π as 3.1415.
The volume of a full sphere cubic cm.
The volume of the half-sphere cubic cm.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume cub cm. This is closest to the third option 385.17 cubic centimeters.
Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
<em>N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.</em>
