Question : A toy is in the shape of a cylinder surmounted by a hemisphere. The total height of the toy is 15 cm and the radius of the hemisphere is 6 cm. What is the volume of the toy?

Option 1: $496\pi$ cm³

Option 2: $476\pi$ cm³

Option 3: $458\pi$ cm³

Option 4: $468\pi$ cm³

Question : Find the volume of a sphere having a diameter of 6 mm, in terms of $\pi$.

Option 1: $12 \pi ~\mathrm{mm}^3$

Option 2: $24 \pi ~\mathrm{mm}^3$

Option 3: $64 \pi~ \mathrm{mm}^3$

Option 4: $36 \pi ~\mathrm{mm}^3$

Question : The radius of a hemisphere is 5 cm. Find the volume.

Option 1: 330.4 cm³

Option 2: 117.9 cm³

Option 3: 150.6 cm³

Option 4: 261.9 cm³

Question : The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle.

Option 1: $1 \sqrt{3} \mathrm{~cm}^2$

Option 2: $6 \sqrt{3} \mathrm{~cm}^2$

Option 3: $3 \sqrt{2} \mathrm{~cm}^2$

Option 4: $4 \sqrt{6} \mathrm{~cm}^2$

Question : A solid copper sphere of radius 6 cm is melted and redrawn into a wire, whose radius of cross-section is 8 cm. Find the length of the wire.

Option 1: 9 cm

Option 2: 2.25 cm

Option 3: 4.5 cm

Option 4: 6 cm