Concept explainers
(a)
To calculate: The total volume of the given
(a)
Answer to Problem 7PSB
The total volume of the given solid is
Explanation of Solution
Given: In the given solid, cone is having height
Formula Used:
Volume of Cone
where r = radius of base of cone
h = height of cone
Volume of Hemisphere
where r = radius of base of hemisphere
Calculation:
As we can see that the solid is formed by placing a cone over the base of hemisphere which means that the radii of the cone and hemisphere would be same. Then,
Total volume of given solid
By using equations (i) and (ii) in equation (iii) we get,
Substituting the given values
Hence, the total volume of the given solid is
(b)
To calculate: The total surface area of the given solid.
(b)
Answer to Problem 7PSB
The total surface area of the given solid is
Explanation of Solution
Given: In the given solid, cone is having height
Formula Used:
Curved Surface Area of Cone
where r = radius of base of the cone
l = slant height of the cone
Slant height of the Cone
where h = height of the cone
Curved Surface Area of Hemisphere
where r = radius of Hemisphere
Calculation: As we can see that the given solid is formed by placing a cone over the base of hemisphere which means that the radii of the cone and hemisphere would be same. So,
Total Surface Area of the given solid
By using equation (i) and (iii) in equation (iv) we get,
Now replacing l in equation (v) by equation (ii),
Hence, the total volume of the given solid is
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