‭1.5hours‬
‭Mathematics‬
‭100 marks‬
‭1. The diameter of a sphere is 16 cm. Calculate its surface area.‬
‭2.‬‭A‬‭cylinder‬‭has‬‭a‬‭volume‬‭of‬‭500π‬‭cubic‬‭centimeters‬‭and‬‭a‬‭height‬‭of‬‭20‬‭cm.‬‭Determine‬
‭its radius.‬
‭3.‬ ‭A‬ ‭cone‬ ‭and‬ ‭a‬ ‭cylinder‬ ‭have‬ ‭the‬ ‭same‬ ‭radius‬ ‭and‬ ‭height.‬‭If‬‭the‬‭volume‬‭of‬‭the‬‭cone‬‭is‬
‭half the volume of the cylinder, find the ratio of their radii.‬
‭4.‬‭A‬‭rectangular‬‭prism‬‭has‬‭a‬‭surface‬‭area‬‭of‬‭400‬‭square‬‭centimeters.‬‭If‬‭its‬‭length‬‭is‬‭twice‬
‭its width and height, find its dimensions.‬
‭5.‬ ‭A‬ ‭hemisphere‬ ‭sits‬ ‭on‬ ‭top‬ ‭of‬ ‭a‬ ‭cylinder.‬ ‭The‬ ‭radius‬ ‭of‬ ‭the‬ ‭hemisphere‬ ‭is‬‭equal‬‭to‬‭the‬
‭radius‬ ‭of‬ ‭the‬ ‭cylinder.‬ ‭If‬ ‭the‬ ‭combined‬ ‭volume‬ ‭of‬ ‭the‬ ‭hemisphere‬ ‭and‬ ‭cylinder‬ ‭is‬ ‭100π‬
‭cubic centimeters, find the height of the cylinder.‬
‭6.‬ ‭A‬ ‭right‬ ‭circular‬ ‭cone‬ ‭has‬ ‭a‬‭volume‬‭of‬‭250π‬‭cubic‬‭centimeters‬‭and‬‭a‬‭height‬‭of‬‭15‬‭cm.‬
‭Determine its radius.‬
‭7.‬‭A‬‭sphere‬‭is‬‭inscribed‬‭in‬‭a‬‭cube‬‭with‬‭a‬‭volume‬‭of‬‭512‬‭cubic‬‭centimeters.‬‭Calculate‬‭the‬
‭surface area of the cube.‬
‭8.‬ ‭The‬ ‭base‬‭of‬‭a‬‭triangular‬‭pyramid‬‭has‬‭sides‬‭of‬‭length‬‭10‬‭cm,‬‭12‬‭cm,‬‭and‬‭14‬‭cm.‬‭If‬‭the‬
‭height of the pyramid is 9 cm, find its volume.‬
‭9.‬‭A‬‭sphere‬‭is‬‭inscribed‬‭in‬‭a‬‭cylinder‬‭such‬‭that‬‭the‬‭diameter‬‭of‬‭the‬‭sphere‬‭is‬‭equal‬‭to‬‭the‬
‭height‬ ‭of‬ ‭the‬ ‭cylinder.‬ ‭If‬ ‭the‬ ‭volume‬ ‭of‬ ‭the‬ ‭cylinder‬ ‭is‬‭400π‬‭cubic‬‭centimeters,‬‭find‬‭the‬
‭radius of the cylinder.‬
‭10.‬ ‭A‬ ‭cone‬ ‭and‬ ‭a‬ ‭hemisphere‬ ‭have‬ ‭the‬ ‭same‬ ‭base‬ ‭radius‬‭and‬‭height.‬‭If‬‭the‬‭total‬‭surface‬
‭area‬ ‭of‬ ‭the‬ ‭hemisphere‬ ‭is‬ ‭200π‬ ‭square‬ ‭centimeters,‬ ‭find‬ ‭the‬ ‭ratio‬ ‭of‬ ‭the‬ ‭volumes‬‭of‬‭the‬
‭cone to the hemisphere.‬