Meena wants to make a toy for her younger brother. The toy is in the shape of a hemisphere surmounted by a cone. If the radius of hemisphere and base radius of cone is 7 cm and height of cone is 3.5 cm. (Take pi = 22/7)
Now answer!
(i) Find the volume of the solid.
(11) Find the cost of painting the whole toy at the rate of Rs.10 per cm².
1. Volume of cone + volume of
hemisphere
1/3 πr^2h + 2/3 πr^3
898.3 is the answer
To find the volume of the solid, we need to calculate the volume of both the hemisphere and the cone, and then add them together.
(i) Volume of Hemisphere:
The formula for the volume of a hemisphere is (2/3) * π * r^3, where r is the radius of the hemisphere. Substituting the given radius (7 cm) into the formula, we get:
Volume of hemisphere = (2/3) * (22/7) * (7)^3 = (2/3) * (22/1) * (343) = 2 * 22 * 49 = 2156 cm^3
(ii) Volume of Cone:
The formula for the volume of a cone is (1/3) * π * r^2 * h, where r is the base radius of the cone, and h is the height of the cone. Substituting the given base radius (7 cm) and height (3.5 cm) into the formula, we get:
Volume of cone = (1/3) * (22/7) * (7)^2 * (3.5) = (1/3) * (22/1) * (49) * (3.5) = 22 * 49/3 * 3.5 = 2156/3 = 718.67 cm^3 (approx.)
So, the total volume of the toy is the sum of the volume of the hemisphere and the volume of the cone:
Total volume = Volume of hemisphere + Volume of cone = 2156 cm^3 + 718.67 cm^3 = 2874.67 cm^3 (approx.)
Now, let's move on to the next question:
(11) To find the cost of painting the whole toy, we need to calculate the total surface area of the toy and then multiply it by the rate of Rs. 10 per cm².
Surface Area of Hemisphere:
The formula for the surface area of a hemisphere is 2πr^2, where r is the radius of the hemisphere. Substituting the given radius (7 cm) into the formula, we get:
Surface Area of hemisphere = 2 * (22/7) * (7)^2 = 2 * (22/1) * 49 = (44/1) * 49 = 2156 cm²
Surface Area of Cone:
The formula for the surface area of a cone is πr(r + √(r^2 + h^2)), where r is the base radius of the cone, and h is the height of the cone. Substituting the given base radius (7 cm) and height (3.5 cm) into the formula, we get:
Surface Area of cone = (22/7) * 7 * (7 + √(7^2 + 3.5^2)) = (22/7) * 7 * (7 + √(49 + 12.25)) = (22/7) * 7 * (7 + √(61.25)) = (22/7) * 7 * (7 + 7.82) = (22/7) * 7 * 14.82 ≈ 310.46 cm²
Total Surface Area of the toy = Surface Area of hemisphere + Surface Area of cone = 2156 cm² + 310.46 cm² ≈ 2466.46 cm²
Finally, to find the cost of painting the whole toy, we multiply the total surface area by the rate of Rs. 10 per cm²:
Cost of painting = Total Surface Area * Rate = 2466.46 cm² * Rs. 10/cm² ≈ Rs. 24664.60 (approx.)
So, the cost of painting the whole toy at the rate of Rs. 10 per cm² is approximately Rs. 24664.60.
No idea kud karo
surely you know by now that the volume of the parts are
cone: 1/3 πr^2 h
hemisphere: 2/3 πr^3
and their areas are:
cone: πrs = πr√(r^2+h^2)
hemisphere: 2πr^2
so plug in your numbers.
You could easily have discovered these formulas online. Just sayin'