The total surface area of a cube of side $$$$ is ______.

$$6a^2$$ A cube has $$6$$ equal faces, each with an area of $$a^2$$ . So, the total surface area is $$6a^2$$ .

The volume of a hemisphere of radius r is $$(2/3)\pi r^3$$ $$True\ or\ False$$

$$True$$ A hemisphere is half of a sphere. The volume of a sphere is $$(4/3)\pi r^3$$ , so the volume of a hemisphere is half of that, which is $$(2/3)\pi r^3$$ .

If two solid shapes have the same volume, they must have the same surface area. $$True\ or\ False$$

$$False$$ Volume and surface area are independent. For example, a long, thin cylinder and a short, fat cylinder can have the same volume but very different surface areas.

The volume of a cylinder with radius $$$$ and height $$$$ is ______.

$$\pi r^2h$$ The volume of a cylinder is the area of its circular base $$(\pi r^2)$$ multiplied by its height $$(h)$$ .

The surface area of a sphere is $$4\pi r^2$$ . $$True\ or\ False$$

$$True$$ This is the standard formula for the surface area of a sphere with radius $$$$ It represents the area of its outer curved surface.

The formula for the slant height $$(l)$$ of a cone, given its height $$(h)$$ and radius $$(r)$$ , is ______.

$$l=\sqrt[]{(r^2+h^2)}$$ The slant height is the hypotenuse of a right-angled triangle with height $$(h)$$ and radius $$(r)$$ as the other two sides.

If the radius of a sphere is doubled, its volume becomes $$4$$ times the original volume. $$True\ or\ False$$

$$False$$ Volume is proportional to the cube of the radius $$(V∝r^3).\ So,(2r)^3=8r^3,$$ meaning the new volume is $$8$$ times the original.

The curved surface area of a cylinder is the same as that of a rectangle with length $$2\pi r$$ and height $$h$$ . $$True\ or\ False$$

$$True$$ If you unroll the curved surface of a cylinder, it forms a rectangle whose length is the circumference of the base $$(2\pi r)$$ and width is the height $$(h)$$ of the cylinder.

The total surface area of a hemisphere of radius $$$$ is ______.

$$3\pi r^2$$ It includes the curved surface area $$(2\pi r^2)$$ plus the area of the circular base $$(\pi r^2)$$ . So, $$2\pi r^2+\pi r^2=3\pi r^2.$$

The volume of a cone is one-fourth the volume of a cylinder having the same base radius and height. $$True\ or\ False$$

$$False$$ The volume of a cone is one-third the volume of a cylinder with the same base radius and height. $$V_{cylinder}=\pi r^2h$$ $$V_{cone}=\frac{1}{3}\pi r^2h$$

If a wire is bent into the form of a circle, and then bent into a square, the area enclosed will remain the same. $$True\ or\ False$$

$$False$$ For a fixed perimeter, a circle encloses the maximum area. A square with the same perimeter will enclose a smaller area.

The formula for the lateral surface area of a cuboid is $$2(lb+bh+hl)$$ l = length b = breadth h = height $$True\ or\ False$$

$$False$$ $$2(lb+bh+hl)$$ is the total surface area. The lateral (or curved) surface area is $$2h(l+b)$$ The LSA is the combined area of the four vertical walls of a cuboid shape, like the walls of a room (excluding the floor and the ceiling).

The ratio of the volumes of two spheres is $$8:27$$ . The ratio of their surface areas is ______.

$$4:9$$ Ratio of Volume = $$\left(\frac{r_1}{r_2}\right)^2=\frac{8}{27}$$ Gives - $$\frac{r_1}{r_2}=\frac{2}{3}$$ Ratio of Surface $$\frac{r_1}{r_2}=\left(\frac{2}{3}\right)^2$$

FC-CBSE-10-M-C12 Flashcards

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2.

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3.

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The curved surface area of a right circular cone with base radius r and slant height l is given by ______.

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4.

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5.

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6.

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When a cone is cut by a plane parallel to its base, the part that contains the base is called a ______ of the cone.

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7.

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